[
  {
    "path": ".gitignore",
    "content": "*.DS_Store\noctave/\nexercises/\n__pycache__/\n*.pyc\n*.swp\n*.swo\n.ipynb_checkpoints\nenv/\n"
  },
  {
    "path": "README.md",
    "content": "# Stanford CS229 Machine Learning in Python\n\nThis repository contains the problem sets for Stanford CS229 (Machine Learning) on Coursera translated to Python 3. It also contains some of my notes.\n\nCheck out the [course website](http://cs229.stanford.edu/) and the [Coursera course](https://www.coursera.org/learn/machine-learning). Please note that your solutions won't be graded and this repo is not affiliated with Coursera or Stanford in any way.\n\n## Installation\n\nMake sure you have jupyter notebooks installed. You can find instructions [here](https://jupyter.org/install).\n\nThe following Python packages are used:\n\n- [Numpy](https://www.numpy.org)\n- [Scipy](https://www.scipy.org)\n- [Matplotlib](https://matplotlib.org)\n- [Pandas](https://pandas.pydata.org)\n- [Pillow](https://python-pillow.org)\n- [Natural Language Toolkit](http://www.nltk.org)\n\nYou can install all dependencies using:\n\n```shell\npython3 -m pip install -r requirements.txt\n```\n\n## Instructions\n\n1. Please download the exercises (pdf) from the Coursera course. Some instructions are included in the Notebooks.\n2. Complete the exercises in the exercises Notebook.\n3. Compare your answers to the code in solutions Notebook.\n\n## Contents\n\n1. Linear Regression\n2. Logistic Regression & Regularization\n3. Multiclass Classifcation & Neural Networks\n4. Neueral Networks Learning\n5. Regularized Linear Regression and Bias v.s. Variance\n6. Support Vector Machines\n7. K-means Clustering and Principal Component Analysis\n8. Anomaly Detection and Recommender Systems\n\n## Copyright Notice\n\nAll code, exercises, data and other files in this repo are ©Stanford University. If you are unhappy about me hosting these files on GitHub for educational purposes, please send me an email.\n\nThe code was 'translated' to Python by Rick Wierenga. Some of the instructions are modified to better fit the Python ecosystem by me too. The data, background information and the intended exercise are the same.\n\n### Solutions\n\nAt the request of Stanford staff, I removed the notebooks with solutions from this repository. The exercises and notes are still available.\n\n---\n\n©2020 Rick Wierenga\n"
  },
  {
    "path": "ex1/PE1 - Linear Regression (Exercises).ipynb",
    "content": "{\n \"cells\": [\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"# Linear Regression\\n\",\n    \"\\n\",\n    \"Stanford CS229 - Machine Learning by Andrew Ng. Programming exercise 1.\\n\",\n    \"\\n\",\n    \"Please check out [the repository on GitHub](https://github.com/rickwierenga/CS229-Python/). If you spot any mistakes or inconcistencies, please create an issue. For questions you can find me on Twitter: [@rickwierenga](https://twitter.com/rickwierenga). Starring the project on GitHub means a ton to me!\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 1,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"import numpy as np\\n\",\n    \"import pandas as pd\\n\",\n    \"import matplotlib.pylab as plt\\n\",\n    \"%matplotlib inline\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Linear Regression with a single variable\\n\",\n    \"---\\n\",\n    \"In this part of this exercise, you will implement linear regression with one variable to predict profits for a food truck. Suppose you are the CEO of a restaurant franchise and are considering different cities for opening a new outlet. The chain already has trucks in various cities and you have data for profits and populations from the cities. You would like to use this data to help you select which city to expand to next. \"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 2,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/html\": [\n       \"<div>\\n\",\n       \"<style scoped>\\n\",\n       \"    .dataframe tbody tr th:only-of-type {\\n\",\n       \"        vertical-align: middle;\\n\",\n       \"    }\\n\",\n       \"\\n\",\n       \"    .dataframe tbody tr th {\\n\",\n       \"        vertical-align: top;\\n\",\n       \"    }\\n\",\n       \"\\n\",\n       \"    .dataframe thead th {\\n\",\n       \"        text-align: right;\\n\",\n       \"    }\\n\",\n       \"</style>\\n\",\n       \"<table border=\\\"1\\\" class=\\\"dataframe\\\">\\n\",\n       \"  <thead>\\n\",\n       \"    <tr style=\\\"text-align: right;\\\">\\n\",\n       \"      <th></th>\\n\",\n       \"      <th>Population</th>\\n\",\n       \"      <th>Profit</th>\\n\",\n       \"    </tr>\\n\",\n       \"  </thead>\\n\",\n       \"  <tbody>\\n\",\n       \"    <tr>\\n\",\n       \"      <th>0</th>\\n\",\n       \"      <td>6.1101</td>\\n\",\n       \"      <td>17.5920</td>\\n\",\n       \"    </tr>\\n\",\n       \"    <tr>\\n\",\n       \"      <th>1</th>\\n\",\n       \"      <td>5.5277</td>\\n\",\n       \"      <td>9.1302</td>\\n\",\n       \"    </tr>\\n\",\n       \"    <tr>\\n\",\n       \"      <th>2</th>\\n\",\n       \"      <td>8.5186</td>\\n\",\n       \"      <td>13.6620</td>\\n\",\n       \"    </tr>\\n\",\n       \"    <tr>\\n\",\n       \"      <th>3</th>\\n\",\n       \"      <td>7.0032</td>\\n\",\n       \"      <td>11.8540</td>\\n\",\n       \"    </tr>\\n\",\n       \"    <tr>\\n\",\n       \"      <th>4</th>\\n\",\n       \"      <td>5.8598</td>\\n\",\n       \"      <td>6.8233</td>\\n\",\n       \"    </tr>\\n\",\n       \"  </tbody>\\n\",\n       \"</table>\\n\",\n       \"</div>\"\n      ],\n      \"text/plain\": [\n       \"   Population   Profit\\n\",\n       \"0      6.1101  17.5920\\n\",\n       \"1      5.5277   9.1302\\n\",\n       \"2      8.5186  13.6620\\n\",\n       \"3      7.0032  11.8540\\n\",\n       \"4      5.8598   6.8233\"\n      ]\n     },\n     \"execution_count\": 2,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"# start by loading the data\\n\",\n    \"data = pd.read_csv('ex1data1.txt', header=None, names=['Population', 'Profit'])\\n\",\n    \"\\n\",\n    \"# initialize some useful variables\\n\",\n    \"m = len(data) # the number of training examples\\n\",\n    \"X = np.append(np.ones((m, 1)), np.array(data[\\\"Population\\\"]).reshape((m,1)), axis=1) # Add x0, a vector of 1's, to X.\\n\",\n    \"y = np.array(data[\\\"Profit\\\"]).reshape(m, 1)\\n\",\n    \"\\n\",\n    \"data.head()\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Visualising the data\\n\",\n    \"Plotting helps us get insight in the data we are working with. Using the `'bx'` option, we get blue crosses. You can read more about markers [here](https://matplotlib.org/api/markers_api.html).\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 3,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"Text(0.5, 1.0, 'Relation between profit and population')\"\n      ]\n     },\n     \"execution_count\": 3,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"plt.plot(data['Population'], data['Profit'], 'bx')\\n\",\n    \"plt.xlabel('Population in 10,000')\\n\",\n    \"plt.ylabel('Profit in $10,000')\\n\",\n    \"plt.title('Relation between profit and population')\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### The hypotheses function\\n\",\n    \"Our hypothesis function has the general form:\\n\",\n    \"$y= h_\\\\theta(x)= \\\\theta_0 + \\\\theta_1x$\\n\",\n    \"Note that this is like the equation of a straight line. We give to $h_\\\\theta(x)$ values for $\\\\theta_0$ and $\\\\theta_1$ to get our estimated output y. In other words, we are trying to create a function called $h_\\\\theta$ that is trying to map our input data (the x's) to our output data (the y's).\\n\",\n    \"\\n\",\n    \"### Cost function\\n\",\n    \"\\n\",\n    \"The cost functions yields \\\"how far off\\\" our hypotheses $h_\\\\theta$ is. It takes the avarage of the distance between our hypothesis and the actual point and squares it. Formally, the cost function has the following definition:\\n\",\n    \"\\n\",\n    \"$J(\\\\theta) = \\\\frac{1}{2m} \\\\displaystyle\\\\sum_{i = 0}^{m}(h_θ(x^{(i)}) - y^{(i)})^2$\\n\",\n    \"\\n\",\n    \"#### Vectorization\\n\",\n    \"Vectorizations is the act of replacing the loops in a computer program with matrix operations. If you have a good linear algebra library (like numpy), the library will optimize the code automatically for the computer the code runs on. Mathematically, the 'regular' function should mean the same as the vectorized function.\\n\",\n    \"\\n\",\n    \"Gradient descent vectorized:\\n\",\n    \"$\\\\theta = \\\\frac{1}{2m}(X\\\\theta - \\\\vec{y})^T(X\\\\theta-\\\\vec{y})$\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement a vectorized implementation of the cost function.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 4,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def cost_function(X, y, theta):\\n\",\n    \"    \\\"\\\"\\\" Computes the cost of using theta as the parameter for linear gression to fit the data in X and y. \\\"\\\"\\\"\\n\",\n    \"    \\n\",\n    \"    return 0\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"With $\\\\theta = \\\\begin{bmatrix}0 & 0\\\\end{bmatrix}$, $J(\\\\theta)$ should return 32.07.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 5,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"0\\n\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"initial_theta = np.zeros((2,1))\\n\",\n    \"print(cost_function(X, y, initial_theta))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Gradient descent\\n\",\n    \"We want are hypothesis $h_\\\\theta(x)$ to function as good as possibly. Therefore, we want to minimalize the cost function $J(\\\\theta)$. Gradient descent is an algorithm used to do that. \\n\",\n    \"\\n\",\n    \"The formal definition of gradient descent:\\n\",\n    \"\\n\",\n    \"$repeat \\\\ \\\\{ \\\\\\\\ \\\\enspace \\\\theta_j := \\\\theta_j - \\\\alpha \\\\frac{1}{m}\\\\displaystyle\\\\sum_{i = 1}^{m}(h_\\\\theta(x^{(i)})-y^{(i)})x_j^{(i)}\\\\\\\\\\\\}$\\n\",\n    \"\\n\",\n    \"An illustration of gradient descent on a single variable:\\n\",\n    \"<div>\\n\",\n    \"    <img style='max-width:50%;' src='notes/gradientdescent.png'>\\n\",\n    \"</div>\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement the gradient descent algorithm in Python.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 6,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def gradient_descent(X, y, theta, alpha, iterations):\\n\",\n    \"    \\\"\\\"\\\" Performs gradient descent to learn theta. \\n\",\n    \"    Returns the found value for theta and the history of the cost function.\\n\",\n    \"    \\\"\\\"\\\"\\n\",\n    \"    J_history = []\\n\",\n    \"    return theta, J_history\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Gradient descent should have found approximately the following: $\\\\theta = \\\\begin{bmatrix}-3.6303\\\\\\\\1.1664\\\\end{bmatrix}$\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 7,\n   \"metadata\": {\n    \"scrolled\": true\n   },\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"array([[0.],\\n\",\n       \"       [0.]])\"\n      ]\n     },\n     \"execution_count\": 7,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"# You can change different values for these variables\\n\",\n    \"alpha = 0.01\\n\",\n    \"iterations = 1500\\n\",\n    \"\\n\",\n    \"theta, J_history = gradient_descent(X, y, initial_theta, alpha, iterations)\\n\",\n    \"theta\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Using the results\\n\",\n    \"#### Plotting the regularization line\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 8,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"[<matplotlib.lines.Line2D at 0x11426d940>]\"\n      ]\n     },\n     \"execution_count\": 8,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"plt.plot(X[:,1], y, 'rx', label='Training data')\\n\",\n    \"plt.plot(X[:,1], X.dot(theta), label='Linear regression')\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"#### Plotting the cost history\\n\",\n    \"A plot of how $J(\\\\theta)$ decreases over time. This is are model learning.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 9,\n   \"metadata\": {\n    \"scrolled\": true\n   },\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"[<matplotlib.lines.Line2D at 0x11438eeb8>]\"\n      ]\n     },\n     \"execution_count\": 9,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"plt.plot(J_history)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"#### Making a prediction using the model\\n\",\n    \"The model can be used by calculating the dot product of the input and $\\\\theta$.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 10,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"'In a city with a population of 35000, we predict a profit of $0.00'\"\n      ]\n     },\n     \"execution_count\": 10,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"prediction = np.array([1, 3.5]).dot(theta) * 10000 # don't forget to multiply the prediction by 10000\\n\",\n    \"'In a city with a population of 35000, we predict a profit of $%.2f' % prediction\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"\\n\",\n    \"## Multivariate Linear Regression\\n\",\n    \"\\n\",\n    \"---\\n\",\n    \"In this part, you will implement linear regression with multiple variables to predict the prices of houses. Suppose you are selling your house and you want to know what a good market price would be. One way to do this is to first collect information on recent houses sold and make a model of housing prices.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 11,\n   \"metadata\": {\n    \"scrolled\": true\n   },\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/html\": [\n       \"<div>\\n\",\n       \"<style scoped>\\n\",\n       \"    .dataframe tbody tr th:only-of-type {\\n\",\n       \"        vertical-align: middle;\\n\",\n       \"    }\\n\",\n       \"\\n\",\n       \"    .dataframe tbody tr th {\\n\",\n       \"        vertical-align: top;\\n\",\n       \"    }\\n\",\n       \"\\n\",\n       \"    .dataframe thead th {\\n\",\n       \"        text-align: right;\\n\",\n       \"    }\\n\",\n       \"</style>\\n\",\n       \"<table border=\\\"1\\\" class=\\\"dataframe\\\">\\n\",\n       \"  <thead>\\n\",\n       \"    <tr style=\\\"text-align: right;\\\">\\n\",\n       \"      <th></th>\\n\",\n       \"      <th>Size</th>\\n\",\n       \"      <th>Bedrooms</th>\\n\",\n       \"      <th>Price</th>\\n\",\n       \"    </tr>\\n\",\n       \"  </thead>\\n\",\n       \"  <tbody>\\n\",\n       \"    <tr>\\n\",\n       \"      <th>0</th>\\n\",\n       \"      <td>2104</td>\\n\",\n       \"      <td>3</td>\\n\",\n       \"      <td>399900</td>\\n\",\n       \"    </tr>\\n\",\n       \"    <tr>\\n\",\n       \"      <th>1</th>\\n\",\n       \"      <td>1600</td>\\n\",\n       \"      <td>3</td>\\n\",\n       \"      <td>329900</td>\\n\",\n       \"    </tr>\\n\",\n       \"    <tr>\\n\",\n       \"      <th>2</th>\\n\",\n       \"      <td>2400</td>\\n\",\n       \"      <td>3</td>\\n\",\n       \"      <td>369000</td>\\n\",\n       \"    </tr>\\n\",\n       \"    <tr>\\n\",\n       \"      <th>3</th>\\n\",\n       \"      <td>1416</td>\\n\",\n       \"      <td>2</td>\\n\",\n       \"      <td>232000</td>\\n\",\n       \"    </tr>\\n\",\n       \"    <tr>\\n\",\n       \"      <th>4</th>\\n\",\n       \"      <td>3000</td>\\n\",\n       \"      <td>4</td>\\n\",\n       \"      <td>539900</td>\\n\",\n       \"    </tr>\\n\",\n       \"  </tbody>\\n\",\n       \"</table>\\n\",\n       \"</div>\"\n      ],\n      \"text/plain\": [\n       \"   Size  Bedrooms   Price\\n\",\n       \"0  2104         3  399900\\n\",\n       \"1  1600         3  329900\\n\",\n       \"2  2400         3  369000\\n\",\n       \"3  1416         2  232000\\n\",\n       \"4  3000         4  539900\"\n      ]\n     },\n     \"execution_count\": 11,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"# load data\\n\",\n    \"data = pd.read_csv(\\\"ex1data2.txt\\\", header = None, names=[\\\"Size\\\", \\\"Bedrooms\\\",\\\"Price\\\"])\\n\",\n    \"m = len(data)\\n\",\n    \"\\n\",\n    \"# Initialize X, y and theta\\n\",\n    \"x0 = np.ones(m)\\n\",\n    \"size = np.array((data[\\\"Size\\\"]))\\n\",\n    \"bedrooms = np.array((data[\\\"Bedrooms\\\"]))\\n\",\n    \"X = np.array([x0, size, bedrooms]).T\\n\",\n    \"y = np.array(data[\\\"Price\\\"]).reshape(len(data.index), 1)\\n\",\n    \"theta_init = np.zeros((3,1))\\n\",\n    \"\\n\",\n    \"data.head()\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Feature Normalization\\n\",\n    \"When features differ by order of magnitude, first performing feature scaling can make gradient descent converge much more quickly. Formally:\\n\",\n    \"\\n\",\n    \"$x := \\\\frac{x - \\\\mu}{\\\\sigma}$\\n\",\n    \"\\n\",\n    \"Where $\\\\mu$ is the average and $\\\\sigma$ the standard deviation.\\n\",\n    \"\\n\",\n    \"**Important**: It is crucial to store $\\\\mu$ and $\\\\sigma$ if you want to make predictions using the model later.\\n\",\n    \"\\n\",\n    \"**Exercise**: Perform feature normalization on the following dataset.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 12,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"array([[1.000e+00, 2.104e+03, 3.000e+00],\\n\",\n       \"       [1.000e+00, 1.600e+03, 3.000e+00],\\n\",\n       \"       [1.000e+00, 2.400e+03, 3.000e+00],\\n\",\n       \"       [1.000e+00, 1.416e+03, 2.000e+00],\\n\",\n       \"       [1.000e+00, 3.000e+03, 4.000e+00]])\"\n      ]\n     },\n     \"execution_count\": 12,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"# perform normalization\\n\",\n    \"def normalize(X):\\n\",\n    \"    \\\"\\\"\\\" Normalizes the features in X\\n\",\n    \"    \\n\",\n    \"    returns a normalized version of X where\\n\",\n    \"    the mean value of each feature is 0 and the standard deviation\\n\",\n    \"    is 1. This is often a good preprocessing step to do when\\n\",\n    \"    working with learning algorithms.\\n\",\n    \"    \\\"\\\"\\\"\\n\",\n    \"    mu = np.zeros(len(X))\\n\",\n    \"    sigma = np.zeros(len(X))\\n\",\n    \"        \\n\",\n    \"    return X, mu, sigma\\n\",\n    \"\\n\",\n    \"X, mu, sigma = normalize(X)\\n\",\n    \"X[0:5]\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Gradient Descent\\n\",\n    \"\\n\",\n    \"Remember the algorithm for gradient descent:\\n\",\n    \"\\n\",\n    \"$repeat \\\\ \\\\{ \\\\\\\\ \\\\enspace \\\\theta_j := \\\\theta_j - \\\\alpha \\\\frac{1}{m}\\\\displaystyle\\\\sum_{i = 1}^{m}(h_\\\\theta(x^{(i)})-y^{(i)})x_j^{(i)}\\\\\\\\\\\\}$\\n\",\n    \"\\n\",\n    \"The vectorization for multivariate gradient descent:\\n\",\n    \"\\n\",\n    \"$\\\\theta := \\\\theta - \\\\frac{\\\\alpha}{m}X^T(X\\\\theta - \\\\vec{y})$\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement gradient descent for multiple features. Make sure your solution is vectorized and supports any number of features.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 13,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"array([[0.],\\n\",\n       \"       [0.],\\n\",\n       \"       [0.]])\"\n      ]\n     },\n     \"execution_count\": 13,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"def gradient_descent_multi(X, y, theta, alpha, iterations):\\n\",\n    \"    J_history = []\\n\",\n    \"    return theta, J_history\\n\",\n    \"\\n\",\n    \"alpha = 0.01\\n\",\n    \"iterations = 1500\\n\",\n    \"initial_theta = np.zeros((3,1))\\n\",\n    \"theta, J_history = gradient_descent_multi(X, y, initial_theta, alpha, iterations)\\n\",\n    \"theta\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"As before we see how the cost decreases over time.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 14,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"Text(0, 0.5, 'cost')\"\n      ]\n     },\n     \"execution_count\": 14,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"plt.plot(J_history)\\n\",\n    \"plt.title('J per iteration')\\n\",\n    \"plt.xlabel('iteration')\\n\",\n    \"plt.ylabel('cost')\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"If we want to make a prediction on a normalized dataset, we have to normalize our input too.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 15,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stderr\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/ipykernel_launcher.py:1: RuntimeWarning: divide by zero encountered in double_scalars\\n\",\n      \"  \\\"\\\"\\\"Entry point for launching an IPython kernel.\\n\"\n     ]\n    },\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"'In a house of 1650 square feet with 3 rooms, we predict a price of $nan'\"\n      ]\n     },\n     \"execution_count\": 15,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"price = theta.transpose() @ np.array([1, (1650-mu[1])/sigma[1], (3-mu[2])/sigma[2]]) # normalize the input\\n\",\n    \"'In a house of 1650 square feet with 3 rooms, we predict a price of $%.2f' % price\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Using normal equations\\n\",\n    \"We can use normal equations to get the exact solution in only one calculation. Although using normal equations is very fast for a small datasets with a small number of features, it can be inefficient for larger datasets because the complexity of matrix multiplication is $O(n^3)$.\\n\",\n    \"\\n\",\n    \"The normal equation for linear regression is:\\n\",\n    \"\\n\",\n    \"$\\\\theta = 􏰅 (X^TX)^{−1}X^T\\\\vec{y}$\\n\",\n    \"\\n\",\n    \"**Exercise**: Find theta using normal equations.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 16,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"array([[89597.9095428 ],\\n\",\n       \"       [  139.21067402],\\n\",\n       \"       [-8738.01911233]])\"\n      ]\n     },\n     \"execution_count\": 16,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"theta\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 17,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stderr\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/ipykernel_launcher.py:1: RuntimeWarning: divide by zero encountered in double_scalars\\n\",\n      \"  \\\"\\\"\\\"Entry point for launching an IPython kernel.\\n\"\n     ]\n    },\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"'In a house of 1650 square feet with 3 rooms, we predict a price of $nan'\"\n      ]\n     },\n     \"execution_count\": 17,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"price = theta.transpose() @ np.array([1, (1650-mu[1])/sigma[1], (3-mu[2])/sigma[2]]) # normalize the input\\n\",\n    \"'In a house of 1650 square feet with 3 rooms, we predict a price of $%.2f' % price\"\n   ]\n  }\n ],\n \"metadata\": {\n  \"kernelspec\": {\n   \"display_name\": \"Python 3\",\n   \"language\": \"python\",\n   \"name\": \"python3\"\n  },\n  \"language_info\": {\n   \"codemirror_mode\": {\n    \"name\": \"ipython\",\n    \"version\": 3\n   },\n   \"file_extension\": \".py\",\n   \"mimetype\": \"text/x-python\",\n   \"name\": \"python\",\n   \"nbconvert_exporter\": \"python\",\n   \"pygments_lexer\": \"ipython3\",\n   \"version\": \"3.7.1\"\n  }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n"
  },
  {
    "path": "ex1/ex1data1.txt",
    "content": "6.1101,17.592\n5.5277,9.1302\n8.5186,13.662\n7.0032,11.854\n5.8598,6.8233\n8.3829,11.886\n7.4764,4.3483\n8.5781,12\n6.4862,6.5987\n5.0546,3.8166\n5.7107,3.2522\n14.164,15.505\n5.734,3.1551\n8.4084,7.2258\n5.6407,0.71618\n5.3794,3.5129\n6.3654,5.3048\n5.1301,0.56077\n6.4296,3.6518\n7.0708,5.3893\n6.1891,3.1386\n20.27,21.767\n5.4901,4.263\n6.3261,5.1875\n5.5649,3.0825\n18.945,22.638\n12.828,13.501\n10.957,7.0467\n13.176,14.692\n22.203,24.147\n5.2524,-1.22\n6.5894,5.9966\n9.2482,12.134\n5.8918,1.8495\n8.2111,6.5426\n7.9334,4.5623\n8.0959,4.1164\n5.6063,3.3928\n12.836,10.117\n6.3534,5.4974\n5.4069,0.55657\n6.8825,3.9115\n11.708,5.3854\n5.7737,2.4406\n7.8247,6.7318\n7.0931,1.0463\n5.0702,5.1337\n5.8014,1.844\n11.7,8.0043\n5.5416,1.0179\n7.5402,6.7504\n5.3077,1.8396\n7.4239,4.2885\n7.6031,4.9981\n6.3328,1.4233\n6.3589,-1.4211\n6.2742,2.4756\n5.6397,4.6042\n9.3102,3.9624\n9.4536,5.4141\n8.8254,5.1694\n5.1793,-0.74279\n21.279,17.929\n14.908,12.054\n18.959,17.054\n7.2182,4.8852\n8.2951,5.7442\n10.236,7.7754\n5.4994,1.0173\n20.341,20.992\n10.136,6.6799\n7.3345,4.0259\n6.0062,1.2784\n7.2259,3.3411\n5.0269,-2.6807\n6.5479,0.29678\n7.5386,3.8845\n5.0365,5.7014\n10.274,6.7526\n5.1077,2.0576\n5.7292,0.47953\n5.1884,0.20421\n6.3557,0.67861\n9.7687,7.5435\n6.5159,5.3436\n8.5172,4.2415\n9.1802,6.7981\n6.002,0.92695\n5.5204,0.152\n5.0594,2.8214\n5.7077,1.8451\n7.6366,4.2959\n5.8707,7.2029\n5.3054,1.9869\n8.2934,0.14454\n13.394,9.0551\n5.4369,0.61705\n"
  },
  {
    "path": "ex1/ex1data2.txt",
    "content": "2104,3,399900\n1600,3,329900\n2400,3,369000\n1416,2,232000\n3000,4,539900\n1985,4,299900\n1534,3,314900\n1427,3,198999\n1380,3,212000\n1494,3,242500\n1940,4,239999\n2000,3,347000\n1890,3,329999\n4478,5,699900\n1268,3,259900\n2300,4,449900\n1320,2,299900\n1236,3,199900\n2609,4,499998\n3031,4,599000\n1767,3,252900\n1888,2,255000\n1604,3,242900\n1962,4,259900\n3890,3,573900\n1100,3,249900\n1458,3,464500\n2526,3,469000\n2200,3,475000\n2637,3,299900\n1839,2,349900\n1000,1,169900\n2040,4,314900\n3137,3,579900\n1811,4,285900\n1437,3,249900\n1239,3,229900\n2132,4,345000\n4215,4,549000\n2162,4,287000\n1664,2,368500\n2238,3,329900\n2567,4,314000\n1200,3,299000\n852,2,179900\n1852,4,299900\n1203,3,239500\n"
  },
  {
    "path": "ex2/PE2 - Logistic Regression (Exercises).ipynb",
    "content": "{\n \"cells\": [\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"# Linear Regression\\n\",\n    \"\\n\",\n    \"Stanford CS229 - Machine Learning by Andrew Ng. Programming exercise 2 with solutions.\\n\",\n    \"\\n\",\n    \"Please check out [the repository on GitHub](https://github.com/rickwierenga/CS229-Python/). If you spot any mistakes or inconcistencies, please create an issue. For questions you can find me on Twitter: [@rickwierenga](https://twitter.com/rickwierenga). Starring the project on GitHub means a ton to me!\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 1,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"import numpy as np\\n\",\n    \"import pandas as pd\\n\",\n    \"import matplotlib.pylab as plt\\n\",\n    \"%matplotlib inline\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Logistic Regression\\n\",\n    \"\\n\",\n    \"---\\n\",\n    \"Logistic regression is predicting in which category a given data point is. In binary classifiction, there are only two categories:\\n\",\n    \"\\n\",\n    \"$$y \\\\in \\\\{0,1\\\\}$$\\n\",\n    \"\\n\",\n    \"In this exercise, you will implement logistic regression and apply it to two different datasets. Before starting on the programming exercise, we strongly recommend watching the video lectures and completing the review questions for the associated topics.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 2,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"array([[ 1.        , 34.62365962, 78.02469282],\\n\",\n       \"       [ 1.        , 30.28671077, 43.89499752],\\n\",\n       \"       [ 1.        , 35.84740877, 72.90219803],\\n\",\n       \"       [ 1.        , 60.18259939, 86.3085521 ],\\n\",\n       \"       [ 1.        , 79.03273605, 75.34437644]])\"\n      ]\n     },\n     \"execution_count\": 2,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"# start by loading the data\\n\",\n    \"data = pd.read_csv(\\\"ex2data1.txt\\\", header = None, \\n\",\n    \"                   names = [\\\"Exam 1 Score\\\", \\\"Exam 2 Score\\\", \\\"Accepted\\\"])\\n\",\n    \"\\n\",\n    \"# initialize some useful variables\\n\",\n    \"m = len(data[\\\"Accepted\\\"])\\n\",\n    \"x0 = np.ones(m)\\n\",\n    \"size = np.array((data[\\\"Exam 1 Score\\\"]))\\n\",\n    \"bedrooms = np.array((data[\\\"Exam 2 Score\\\"]))\\n\",\n    \"X = np.array([x0, size, bedrooms]).T\\n\",\n    \"y = np.array(data[\\\"Accepted\\\"]).reshape((m,1))\\n\",\n    \"m, n = X.shape\\n\",\n    \"\\n\",\n    \"X[:5]\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Visualising the data\\n\",\n    \"A blue cross means accepted. A yellow oval means rejected.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 3,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"# Find indices of positive and negative examples\\n\",\n    \"pos = np.where(y==1)[0]\\n\",\n    \"neg = np.where(y==0)[0]\\n\",\n    \"\\n\",\n    \"# Plot examples\\n\",\n    \"plt.plot(X[pos, 1], X[pos, 2], 'b+', label='Admitted')\\n\",\n    \"plt.plot(X[neg, 1], X[neg, 2], 'yo', label='Not admitted')\\n\",\n    \"plt.legend()\\n\",\n    \"plt.show()\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Sigmoid\\n\",\n    \"The sigmoid function, or logistic function, is a function that asymptotes at 0 and 1. The value at 0 is $\\\\frac{1}{2}$.\\n\",\n    \"\\n\",\n    \"$h_\\\\theta(x) = g(\\\\theta^Tx) = g(z) = \\\\frac{1}{1+ e^{-z}} = \\\\frac{1}{1+ e^{-\\\\theta^Tx}}$\\n\",\n    \"\\n\",\n    \"A plot of the sigmoid function:\\n\",\n    \"![sigmoid](notes/sigmoid.png)\\n\",\n    \"\\n\",\n    \"We are going to use the sigmoid function to predict how likely it is that a given data point is in category 0. Our hypothesis:\\n\",\n    \"\\n\",\n    \"$h_\\\\theta(x) = P(y = 0|x;\\\\theta)$\\n\",\n    \"\\n\",\n    \"Because there are only two categories (in this case), we can derrive that:\\n\",\n    \"\\n\",\n    \"$P(y = 0|x;\\\\theta) + P(y = 1|x;\\\\theta)= 1$\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement the sigmoid function in Python.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 4,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def sigmoid(z):\\n\",\n    \"    return z\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Compute the Cost and Gradient\\n\",\n    \"\\n\",\n    \"#### The cost function\\n\",\n    \"\\n\",\n    \"The cost function in logistic regression differs from the one used in linear regression. The cost function in logistic regression:\\n\",\n    \"\\n\",\n    \"$$J(\\\\theta) = - \\\\begin{bmatrix}\\\\frac{1}{m}\\\\displaystyle\\\\sum_{i=1}^{m}-y^{(i)}\\\\log h(x^{(i)}-(1-y^{(i)})\\\\log(1-h_\\\\theta(x^{(i)}))\\\\end{bmatrix}$$\\n\",\n    \"\\n\",\n    \"Assume our hypothesis for an example is wrong, the higher probability $h_\\\\theta$ had predicted, the higher the penatly.\\n\",\n    \"\\n\",\n    \"A vectorized version of the cost function:\\n\",\n    \"\\n\",\n    \"$$J(\\\\theta) = \\\\frac{1}{m} ⋅(−y^T \\\\log(h)−(1−y)^T \\\\log(1−h))$$\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement the vectorized cost function in Python.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 5,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def compute_cost(theta, X, y):\\n\",\n    \"    return 0\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"#### The gradient\\n\",\n    \"\\n\",\n    \"The gradient is the step a minimization algorithm, like gradient descent, takes to get to the (local) minimum. Note that this step can be taken in a higher dimension and hence the gradient is a vector. In the previous programming exercise we used gradient descent. This time, we are going to use an algorithm called conjugate gradient to find the minimum. How that algorithm works is beyond the scope if this course. If you are interested, you can learn more about it [here](https://en.wikipedia.org/wiki/Conjugate_gradient_method).\\n\",\n    \"\\n\",\n    \"The partial derrivative or $J(\\\\theta)$:\\n\",\n    \"\\n\",\n    \"$$\\\\frac{\\\\delta}{\\\\delta\\\\theta_J} = \\\\frac{1}{m}\\\\displaystyle\\\\sum_{i = 1}^{m} \\\\begin{bmatrix}(h_\\\\theta(x^{(i)}) - y^{(i)}\\\\end{bmatrix}x_j^{(i)}$$\\n\",\n    \"\\n\",\n    \"Vectorized:\\n\",\n    \"\\n\",\n    \"$$\\\\frac{\\\\delta}{\\\\delta\\\\theta_J} = \\\\frac{1}{m} \\\\cdot X^T \\\\cdot (g(X\\\\cdot\\\\theta)-\\\\vec{y})$$\\n\",\n    \"\\n\",\n    \"**Exercise**: Write a function to compute the gradient.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 6,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def compute_gradient(theta, X, y):\\n\",\n    \"    return np.zeros(len(theta))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Test the cost and gradient function. We expect $J \\\\approx 0.693$ and $\\\\frac{\\\\delta}{\\\\delta\\\\theta_J} \\\\approx \\\\begin{bmatrix}-0.1000 & -12.0092 & -11.2628 \\\\end{bmatrix}$\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 7,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"Cost: \\n\",\n      \"0.6931471805599453\\n\",\n      \"\\n\",\n      \"Gradient: \\n\",\n      \"[ -0.1        -12.00921659 -11.26284221]\\n\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"initial_theta = np.zeros(n)\\n\",\n    \"y = y.reshape(m)\\n\",\n    \"print('Cost: \\\\n{}\\\\n'.format(compute_cost(initial_theta, X, y)))\\n\",\n    \"print('Gradient: \\\\n{}'.format(compute_gradient(initial_theta, X, y)))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Learning $\\\\theta$ using conjugate gradient\\n\",\n    \"\\n\",\n    \"The optimization library we are going to use is `scipy.optimize`. We have to provide the algorithm with our cost function, initial guess, gradient among with some other (optional) configuration options.\\n\",\n    \"\\n\",\n    \"Please scan [the docs](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html) of `minimize` first.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 8,\n   \"metadata\": {\n    \"scrolled\": true\n   },\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"Optimization terminated successfully.\\n\",\n      \"         Current function value: 0.203498\\n\",\n      \"         Iterations: 42\\n\",\n      \"         Function evaluations: 100\\n\",\n      \"         Gradient evaluations: 100\\n\",\n      \"Conjugate gradient found the following values for theta: [-25.15522426   0.20618292   0.20142209]\\n\"\n     ]\n    },\n    {\n     \"name\": \"stderr\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/ipykernel_launcher.py:3: RuntimeWarning: divide by zero encountered in log\\n\",\n      \"  This is separate from the ipykernel package so we can avoid doing imports until\\n\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"from scipy.optimize import minimize\\n\",\n    \"result = minimize(compute_cost, initial_theta, args = (X, y),\\n\",\n    \"                   method = 'CG', jac = compute_gradient, \\n\",\n    \"                   options = {\\\"maxiter\\\": 400, \\\"disp\\\" : 1})\\n\",\n    \"theta = result.x\\n\",\n    \"print('Conjugate gradient found the following values for theta: {}'.format(theta))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### The decision boundary\\n\",\n    \"The decision boundary is a line (in case of a 2d plane) that seperates the area where we predict $y=1$ and $y=0$.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 9,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"<matplotlib.legend.Legend at 0x120189cc0>\"\n      ]\n     },\n     \"execution_count\": 9,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"# Find indices of positive and negative examples\\n\",\n    \"pos = np.where(y==1)[0]\\n\",\n    \"neg = np.where(y==0)[0]\\n\",\n    \"\\n\",\n    \"# Plot examples\\n\",\n    \"plt.plot(X[pos, 1], X[pos, 2], 'b+', label='Admitted')\\n\",\n    \"plt.plot(X[neg, 1], X[neg, 2], 'yo', label='Not admitted')\\n\",\n    \"plt.legend()\\n\",\n    \"\\n\",\n    \"# Plot the decision boundary\\n\",\n    \"plot_x = np.array([min(X[:,1])-2,  max(X[:,1])+2])\\n\",\n    \"plot_y = (-1./theta[2]) * ((theta[1] * (plot_x) + theta[0]))\\n\",\n    \"\\n\",\n    \"plt.plot(plot_x, plot_y, label='Decision boundary')\\n\",\n    \"\\n\",\n    \"# Legend, specific for the exercise\\n\",\n    \"plt.legend()\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Evaluation\\n\",\n    \"#### Probability that a given student will be admitted\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 10,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"For a student with scores 45 and 85, we predict an admission probability of 0.78\\n\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"prob = sigmoid(np.array([1, 45, 85]).dot(theta))\\n\",\n    \"print('For a student with scores 45 and 85, we predict an admission probability of {:.2}'.format(prob))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"#### Accuracy\\n\",\n    \"It's often a good idea to see how well your model trained. You can do that by checking how much datapoints we can predict correctly using $\\\\theta$. In a real world application, you should consider splitting your data (eg 80% - 20%) and test on data the model has not seen before. This gives you more realistic insight in how your model would perform in the real world - and that's your ultimate goal ;)\\n\",\n    \"\\n\",\n    \"In this example, we expect a training accuracy of 89.0%.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 11,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"Training Accuracy: 89.0%\\n\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"p = np.zeros((m, 1))\\n\",\n    \"for (i, example) in enumerate(X):\\n\",\n    \"    prob = sigmoid(np.array(example.dot(theta)))\\n\",\n    \"    if prob >= 0.5:\\n\",\n    \"        p[i] = 1\\n\",\n    \"    else:\\n\",\n    \"        p[i] = 0\\n\",\n    \"print('Training Accuracy: {}%'.format(np.mean(p == y.reshape((m, 1))) * 100))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Regularized linear regression\\n\",\n    \"\\n\",\n    \"---\\n\",\n    \"Regularization is a meganism for preventing overfitting. _Overfitting_ means that our model works extremely well on the training set but bad in the real world. It's focussed on the training data. _Underfitting_ is either a not well trained model or the feature mapping is not done (correctly). We will use regularization in this exercise. Furtermore, we are going to look at a more complex decision boundary\\n\",\n    \"\\n\",\n    \"In this part of the exercise, you will implement regularized logistic regression to predict whether microchips from a fabrication plant passes quality assur- ance (QA). During QA, each microchip goes through various tests to ensure it is functioning correctly.\\n\",\n    \"\\n\",\n    \"Suppose you are the product manager of the factory and you have the test results for some microchips on two different tests. From these two tests, you would like to determine whether the microchips should be accepted or rejected. To help you make the decision, you have a dataset of test results on past microchips, from which you can build a logistic regression model.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 12,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"array([[ 0.051267,  0.69956 ],\\n\",\n       \"       [-0.092742,  0.68494 ],\\n\",\n       \"       [-0.21371 ,  0.69225 ],\\n\",\n       \"       [-0.375   ,  0.50219 ],\\n\",\n       \"       [-0.51325 ,  0.46564 ]])\"\n      ]\n     },\n     \"execution_count\": 12,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"# start by loading the data\\n\",\n    \"data = pd.read_csv(\\\"ex2data2.txt\\\", header = None, \\n\",\n    \"                   names = [\\\"Test 1\\\", \\\"Test 2\\\", \\\"Status\\\"])\\n\",\n    \"\\n\",\n    \"# initialize some useful variables\\n\",\n    \"m = len(data[\\\"Status\\\"])\\n\",\n    \"size = np.array((data[\\\"Test 1\\\"]))\\n\",\n    \"bedrooms = np.array((data[\\\"Test 2\\\"]))\\n\",\n    \"X = np.array([size, bedrooms]).T # don't add a column of ones yet.\\n\",\n    \"y = np.array(data[\\\"Status\\\"])\\n\",\n    \"\\n\",\n    \"X[:5]\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Visualising the data\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 13,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"# Find indices of positive and negative examples\\n\",\n    \"pos = np.where(y==1)[0]\\n\",\n    \"neg = np.where(y==0)[0]\\n\",\n    \"\\n\",\n    \"# Plot examples\\n\",\n    \"plt.plot(X[pos, 0], X[pos, 1], 'b+', label='Admitted')\\n\",\n    \"plt.plot(X[neg, 0], X[neg, 1], 'yo', label='Not admitted')\\n\",\n    \"plt.legend()\\n\",\n    \"plt.show()\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Feature Mapping\\n\",\n    \"\\n\",\n    \"One way to fit the data better is to create more features from each data point. While the feature mapping allows us to build a more expressive classifier, it also more susceptible to overfitting. This will also add $x_0$.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 14,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def map_feature(X1, X2, degree):\\n\",\n    \"    if not type(X1) == np.ndarray:\\n\",\n    \"        X1 = np.array([X1])\\n\",\n    \"\\n\",\n    \"    if not type(X2) == np.ndarray:\\n\",\n    \"        X2 = np.array([X2])\\n\",\n    \"\\n\",\n    \"    assert X1.shape == X2.shape\\n\",\n    \"    \\n\",\n    \"    out = np.ones((len(X1), 1))\\n\",\n    \"    for i in range(1, degree+1):\\n\",\n    \"        for j in range(i + 1):\\n\",\n    \"            new = (X1 ** (i-j) * X2 ** j).reshape(len(X1), 1)\\n\",\n    \"            out = np.hstack((out, new))\\n\",\n    \"    return out\\n\",\n    \"\\n\",\n    \"X = map_feature(X[:,0], X[:,1], degree=6)\\n\",\n    \"m, n = X.shape\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Computing Cost and Gradient\\n\",\n    \"#### Cost function\\n\",\n    \"Regularization works by penalizing theta. Theta values can be high when an overfit occurs so we prefer to keep them low. $\\\\lambda$ is the regularization parameter. If $\\\\lambda=0$, no regularization happens. If $\\\\lambda$ is some big number, $\\\\theta$ has a very high penalty. Just like the learning rate $\\\\alpha$ you have to try out certain values and see which work.\\n\",\n    \"\\n\",\n    \"The cost function with regularization:\\n\",\n    \"\\n\",\n    \"$$J(\\\\theta) = \\\\frac{1}{m}\\\\displaystyle\\\\sum_{i=1}^{m}-\\\\begin{bmatrix}y^{(i)}\\\\log h(x^{(i)}+(1-y^{(i)}\\\\log(1-h_\\\\theta(x^{(i)})) \\\\end{bmatrix} + \\\\frac{\\\\lambda}{m}\\\\displaystyle\\\\sum_{j=1}^{n}{\\\\theta_j}^2$$\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement the regularized cost function.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 15,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def compute_regularized_cost(theta, X, y, _lambda):\\n\",\n    \"    m = len(y)\\n\",\n    \"    regularization = _lambda / (2 * m) * np.sum(theta[1:] ** 2) #np.squared()???/\\n\",\n    \"    cost = 1/m * (-y @ np.log(sigmoid(X @ theta)) - (1 - y) @ np.log(1 - sigmoid(X@theta)))\\n\",\n    \"    return cost + regularization\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"#### Gradient descent\\n\",\n    \"Gradient descent, just like the cost function, is slightly modified for regularization.\\n\",\n    \"\\n\",\n    \"For $\\\\theta_{j}$ where $j = 0$: \\n\",\n    \"\\n\",\n    \"$$\\\\theta_j := \\\\theta_j -\\\\alpha \\\\begin{bmatrix}\\\\frac{1}{m}\\\\displaystyle\\\\sum_{i=1}^{m}(h_\\\\theta(x^{(i)}-y^{(i)}){x_0}^{(i)}\\\\end{bmatrix}$$\\n\",\n    \"\\n\",\n    \"For $\\\\theta_{j}$ where $j \\\\in \\\\{1, 2, ..., n\\\\} $: \\n\",\n    \"\\n\",\n    \"$$\\\\theta_j := \\\\theta_j -\\\\alpha \\\\begin{bmatrix}\\\\frac{1}{m}\\\\displaystyle\\\\sum_{i=1}^{m}(h_\\\\theta(x^{(i)}-y^{(i)})x_j^{(i)} + \\\\frac{\\\\lambda}{m}{\\\\theta_j} \\\\end{bmatrix}$$\\n\",\n    \"\\n\",\n    \"Note that we don't penalize our bias vector $X_1$.\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement `compute_regularized_gradient`.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 16,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def compute_regularized_gradient(theta, X, y, _lambda):\\n\",\n    \"    return np.zeros(len(theta))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"We expect: $J \\\\approx 0.693$ and the first five values of $\\\\theta$: $\\\\begin{bmatrix} 0.0085 && 0.0188 && 0.0001 && 0.0503 && 0.0115 \\\\end{bmatrix}$\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 17,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"Cost at initial theta (zeros): 2.13\\n\",\n      \"Gradient at initial theta (zeros) - first five values only: \\n\",\n      \"[0.34604507 0.08508073 0.11852457 0.1505916  0.01591449]\\n\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"_lambda = 1\\n\",\n    \"initial_theta = np.ones(n)\\n\",\n    \"\\n\",\n    \"cost = compute_regularized_cost(initial_theta, X, y, _lambda)\\n\",\n    \"grad = compute_regularized_gradient(initial_theta, X, y, _lambda)\\n\",\n    \"\\n\",\n    \"print('Cost at initial theta (zeros): {:.3}'.format(cost))\\n\",\n    \"print('Gradient at initial theta (zeros) - first five values only: \\\\n{}'.format(grad[:5]))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Find an optimimal value for theta using conjugate gradient.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 18,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"Optimization terminated successfully.\\n\",\n      \"         Current function value: 0.529003\\n\",\n      \"         Iterations: 28\\n\",\n      \"         Function evaluations: 76\\n\",\n      \"         Gradient evaluations: 76\\n\",\n      \"Conjugate gradient found the following values for theta - first five values only: [ 1.27278161  0.62533883  1.18105652 -2.02009622 -0.91762258]\\n\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"from scipy.optimize import minimize\\n\",\n    \"result = minimize(compute_regularized_cost, initial_theta, args = (X, y, _lambda),\\n\",\n    \"                  method = 'CG', jac = compute_regularized_gradient, \\n\",\n    \"                  options = {\\\"maxiter\\\": 400, \\\"disp\\\" : 1})\\n\",\n    \"theta = result.x\\n\",\n    \"print('Conjugate gradient found the following values for theta - first five values only: {}'.format(theta[:5]))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Plotting the decision boundary\\n\",\n    \"We can plot a more complex decision boundary using `np.linspace` and `contour`.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 20,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"<matplotlib.contour.QuadContourSet at 0x112c08588>\"\n      ]\n     },\n     \"execution_count\": 20,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"# Find indices of positive and negative examples\\n\",\n    \"pos = np.where(y==1)[0]\\n\",\n    \"neg = np.where(y==0)[0]\\n\",\n    \"\\n\",\n    \"# Plot examples\\n\",\n    \"plt.plot(X[pos, 1], X[pos, 2], 'b+', label='Admitted')\\n\",\n    \"plt.plot(X[neg, 1], X[neg, 2], 'yo', label='Not admitted')\\n\",\n    \"plt.legend()\\n\",\n    \"\\n\",\n    \"# Here is the grid range\\n\",\n    \"u = np.linspace(-1, 1.5, 50).reshape(50)\\n\",\n    \"v = np.linspace(-1, 1.5, 50).reshape(50)\\n\",\n    \"z = np.zeros((len(u), len(v)))\\n\",\n    \"\\n\",\n    \"# Evaluate z = theta*x over the grid\\n\",\n    \"for i in range(len(u)):\\n\",\n    \"    for j in range(len(v)):\\n\",\n    \"        z[i,j] = map_feature(u[i], v[j], degree=6).dot(theta)\\n\",\n    \"\\n\",\n    \"# Plot z = 0\\n\",\n    \"# Notice you need to specify the range [0, 0]\\n\",\n    \"#z = z.reshape(len(u), len(v))\\n\",\n    \"plt.contour(u, v, z.T, 0)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Exploring regularization\\n\",\n    \"As mentioned before, $\\\\lambda$ is used to control the problem of overfitting. In the following graphs, models trained with different values of lambda are shown to give you some intuition on the problem of over/underfitting.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 27,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def create_plot_for_lambda(X, y, _lambda):\\n\",\n    \"    from scipy.optimize import minimize\\n\",\n    \"    result = minimize(compute_regularized_cost, initial_theta, args = (X, y, _lambda),\\n\",\n    \"                      method = 'CG', jac = compute_regularized_gradient, \\n\",\n    \"                      options = {\\\"maxiter\\\": 400, \\\"disp\\\" : 1})\\n\",\n    \"    theta = result.x\\n\",\n    \"    print('Conjugate gradient found the following values for theta - first five values only: {}'.format(theta[:5]))\\n\",\n    \"\\n\",\n    \"    # Find indices of positive and negative examples\\n\",\n    \"    pos = np.where(y==1)[0]\\n\",\n    \"    neg = np.where(y==0)[0]\\n\",\n    \"\\n\",\n    \"    # Plot examples\\n\",\n    \"    plt.plot(X[pos, 1], X[pos, 2], 'b+', label='Admitted')\\n\",\n    \"    plt.plot(X[neg, 1], X[neg, 2], 'yo', label='Not admitted')\\n\",\n    \"    plt.legend()\\n\",\n    \"\\n\",\n    \"    # Here is the grid range\\n\",\n    \"    u = np.linspace(-1, 1.5, 50).reshape(50)\\n\",\n    \"    v = np.linspace(-1, 1.5, 50).reshape(50)\\n\",\n    \"    z = np.zeros((len(u), len(v)))\\n\",\n    \"\\n\",\n    \"    # Evaluate z = theta*x over the grid\\n\",\n    \"    for i in range(len(u)):\\n\",\n    \"        for j in range(len(v)):\\n\",\n    \"            z[i,j] = map_feature(u[i], v[j], degree=6).dot(theta)\\n\",\n    \"\\n\",\n    \"    # Plot z = 0\\n\",\n    \"    # Notice you need to specify the range [0, 0]\\n\",\n    \"    #z = z.reshape(len(u), len(v))\\n\",\n    \"    plt.contour(u, v, z.T, 0)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"#### Overfitting\\n\",\n    \"Remember: overfitting means the model probably only works on the training set and not well in the real world. If you model is overfit, consider adding regularization or choosing a higher value for $\\\\lambda$.\\n\",\n    \"\\n\",\n    \"You can check out other values of $\\\\lambda$ yourself.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 38,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"Warning: Maximum number of iterations has been exceeded.\\n\",\n      \"         Current function value: 0.281767\\n\",\n      \"         Iterations: 400\\n\",\n      \"         Function evaluations: 1435\\n\",\n      \"         Gradient evaluations: 1435\\n\",\n      \"Conjugate gradient found the following values for theta - first five values only: [ 2.53231573 -1.3591363   2.44932572 -6.28390865 -8.54930906]\\n\"\n     ]\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"create_plot_for_lambda(X, y, 0)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"#### Underfitting\\n\",\n    \"Underfitting means the model is not well trained. Having a high $\\\\lambda$ can cause underfitting.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 39,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"Optimization terminated successfully.\\n\",\n      \"         Current function value: 0.648216\\n\",\n      \"         Iterations: 14\\n\",\n      \"         Function evaluations: 29\\n\",\n      \"         Gradient evaluations: 29\\n\",\n      \"Conjugate gradient found the following values for theta - first five values only: [ 0.326144   -0.00815789  0.16580133 -0.44666092 -0.11177511]\\n\"\n     ]\n    },\n    {\n     \"data\": {\n      \"image/png\": \"iVBORw0KGgoAAAANSUhEUgAAAYQAAAD8CAYAAAB3u9PLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvDW2N/gAAIABJREFUeJzt3Xl8VOW9+PHPk20SskICCRBCEmTfguACooCg4r5vpSq2vVxb7e2ibW2tAt7SW6/9XVvtYlXcEReqiAsuKIggKItIWGSLLIFsJJB9n+f3RyYhCTPJZObMnDMz3/frlVeSyZlznjkzeb7n2b5Haa0RQgghwswugBBCCGuQgCCEEAKQgCCEEMJBAoIQQghAAoIQQggHCQhCCCEAgwKCUupZpVSxUmqHi79PV0qVK6W2Ob4eMuK4QgghjBNh0H6eB/4GvNjFNp9rra8w6HhCCCEMZkgLQWu9FigzYl9CCCHMYVQLwR2TlVLfAMeA+7TWOztvoJSaB8wDiI2NnThixAg/Fk8IIQLfli1bjmut+3ryXH8FhK3AYK11lVLqMmA5MLTzRlrrp4CnACZNmqQ3b97sp+IJIURwUEod8vS5fpllpLWu0FpXOX5+H4hUSqX449hCCCHc45eAoJRKU0opx89nO45b6o9jCyGEcI8hXUZKqaXAdCBFKZUPzAciAbTWTwI3AD9WSjUBtcAtWtKsCiGEpRgSELTWt3bz97/RMi1VCBGgGhsbyc/Pp66uzuyiCCA6Opr09HQiIyMN26c/ZxkJIQJYfn4+8fHxZGZm4ugBFibRWlNaWkp+fj5ZWVmG7VdSVwgh3FJXV0dycrIEAwtQSpGcnGx4a00CghDCbRIMrMMX74UEBCGEEIAEBCFEgFm+fDlKKb799lunf587dy7Lli1ze3/Hjh3jhhtuAGDbtm28//77bX9bs2YNX3zxRY/LmJmZyfHjx3v8PLNJQBBC+NSCBcbub+nSpUydOpWlS5casr8BAwa0BRCjAkKgkoAghPCphQuN21dVVRXr1q1j8eLFvPrqq0DLjJt77rmH4cOHM2vWLIqLi9u2z8zM5Le//S05OTlMmjSJrVu3cskllzBkyBCefPJJAA4ePMiYMWNoaGjgoYce4rXXXiMnJ4dHHnmEJ598kscee4ycnBw+//xzSkpKuP766znrrLM466yzWL9+PQClpaVcfPHFjB49mh/96EcE6jIrmXYqhAgYb7/9NrNnz2bYsGEkJyezZcsWDh06xJ49e9i1axdFRUWMGjWKH/zgB23PycjIYNu2bfziF79g7ty5rF+/nrq6OsaMGcNdd93Vtl1UVBQPP/wwmzdv5m9/a1k2VVtbS1xcHPfddx8A3/ve9/jFL37B1KlTOXz4MJdccgm7d+9m4cKFTJ06lYceeoj33nuPxYsX+/fEGEQCghDCcAsWdGwZtE6ImT/fuy6kpUuX8rOf/QyAW265haVLl9LU1MStt95KeHg4AwYM4MILL+zwnKuuugqAsWPHUlVVRXx8PPHx8dhsNk6ePNmj469atYpdu3a1/V5RUUFVVRVr167lzTffBODyyy+nd+/enr9IE0lAEEIYbsGCUxW/UmBED0pZWRmffvopubm5KKVobm5GKcW1117b5fNsNhsAYWFhbT+3/t7U1NSjMtjtdjZu3Eh0dHTPX0AAkDEEIURAWLZsGbfddhuHDh3i4MGDHDlyhKysLJKTk3nttddobm6moKCA1atXe3yM+Ph4KisrXf5+8cUX88QTT7T9vm3bNgAuuOACXnnlFQBWrlzJiRMnPC6DmSQgCCF8av58Y/azdOnS01oD119/PQUFBQwdOpRRo0Zx++23M3nyZI+PMWPGDHbt2kVOTg6vvfYaV155JW+99VbboPLjjz/O5s2bGTduHKNGjWobmJ4/fz5r165l9OjRvPnmm2RkZHj1Ws2irDoaLjfIEcJadu/ezciRI80uhmjH2XuilNqitZ7kyf6khSCEEAKQgCCEEMJBAoIQQghAAoIQQggHCQhCCCEACQhCCCEcJCAIIQKCUop777237fc///nPLOgmD8by5cs7pJrwRE9TWa9YsYI//elPTo///PPPc+zYsR4dvzX5nj9IQBBC+ERR0RI2bMhkzZowNmzIpKhoiVf7s9lsvPnmmz2qnI0ICD111VVXcf/99zs9vicBwZ8kIAghDFdUtIQ9e+ZRX38I0NTXH2LPnnleBYWIiAjmzZvHY489dtrfDh48yIUXXsi4ceOYOXMmhw8f5osvvmDFihX86le/IicnhwMHDnR4zjvvvMM555zDhAkTmDVrFkVFRYDrVNYHDx5kxIgRzJ07l2HDhjFnzhxWrVrFeeedx9ChQ/nqq6+Alkr/nnvuOe34jzzyCJs3b2bOnDnk5ORQW1vLli1bmDZtGhMnTuSSSy6hoKAAgC1btjB+/HjGjx/P3//+d4/PWY9prS35NXHiRC2EsI5du3a5ve0XXwzWq1dz2tcXXwz2+PixsbG6vLxcDx48WJ88eVI/+uijev78+Vprra+44gr9/PPPa621Xrx4sb766qu11lrfcccd+o033nC6v7KyMm2327XWWj/99NP6l7/8pdZa65/+9Kd64cKFWmut3333XQ3okpIS/d133+nw8HC9fft23dzcrM8880x95513arvdrpcvX952zOeee07ffffdTo8/bdo0vWnTJq211g0NDXry5Mm6uLhYa631q6++qu+8806ttdZjx47Vn332mdZa6/vuu0+PHj3a6Wtw9p4Am7WH9a5kOxVCGK6+/nCPHndXQkICt99+O48//jgxMTFtj2/YsKEt/fRtt93Gr3/96273lZ+fz80330xBQQENDQ1kZWUBdJnKOisri7FjxwIwevRoZs6ciVKKsWPHcvDgwR69lj179rBjxw4uuugiAJqbm+nfvz8nT57k5MmTXHDBBW2vZ+XKlT3at6eky0gIYTibzXlyN1eP98TPf/5zFi9eTHV1tVf7+elPf8o999xDbm4u//rXv6irq+v2OZ3TZ7dPrd3TVNpaa0aPHs22bdvYtm0bubm5fPTRRz17EQaTgCBMY/Sgo7CO7OxFhIX16vBYWFgvsrMXeb3vPn36cNNNN3W4K9mUKVPabqm5ZMkSzj//fOD09NXtlZeXM3DgQABeeOGFtseNTGXdVTrt4cOHU1JSwoYNGwBobGxk586dJCUlkZSUxLp169pej79IQBCm8MWgo7CO1NQ5DB/+FDbbYEBhsw1m+PCnSE2dY8j+77333g6zjZ544gmee+45xo0bx0svvcRf//pXoOWuao8++igTJkw4bVB5wYIF3HjjjUycOJGUlJS2x41MZd35+HPnzuWuu+4iJyeH5uZmli1bxm9+8xvGjx9PTk4OX3zxBQDPPfccd999Nzk5OX69P7Okvxam2LAh0xEMOrLZBjN58kH/F8gLRUVLyMt7gPr6w9hsGWRnLzKs4rMSSX9tPUanv5ZBZWEKXw06+ltrS8durwFoa+kAQRkURHCTLiNhCl8OOvpTXt4DbcGgld1eQ17eAyaVSAjPSUAQpvDloKM/BUtLx11W7WIORb54LyQgCFP4etDRX4KlpeOO6OhoSktLJShYgNaa0tJSoqOjDd2vjCEI06Smzgm4ANBZdvaiDmMIEJgtHXekp6eTn59PSUmJ2UURtATo9PR0Q/cpAUEIL7QGtFCYZRQZGdm2mlcEJwkIQngpGFo6QoBBYwhKqWeVUsVKqR0u/q6UUo8rpfYrpbYrpc404rihQlb0yjkQwh+MGlR+Hpjdxd8vBYY6vuYB/zTouEEv2Fb0elKxB9s5EMKqDAkIWuu1QFkXm1wNvOjIzroRSFJK9Tfi2MEumOa5e1qxB9M5EMLK/DXtdCBwpN3v+Y7HOlBKzVNKbVZKbZaZDC2sMM+9m7sUus3Tit0K50CIUGCpdQha66e01pO01pP69u1rdnEswQrz3BcuNGY/nlbsVjgHQoQCfwWEo8Cgdr+nOx4T3QiWFb3gecUeTOdACCvzV0BYAdzumG10LlCutS7w07EDmlkrehcsAKVavuDUz950H3lasfvrHMhMJhHqDEl/rZRaCkwHUoAiYD4QCaC1flIppYC/0TITqQa4U2vdZW5rSX/tPaPSMisFRmUr8FWqaG/32zlrKbQEq0BMpyFCmzfpr+V+CBZlpQrOyIDgC0a81mC6P4MIbd4EBEsNKosWRsy7N3Kq5vz5PX6KXxnxWkN1JpN0k4n2JCBYkNUqOKOmnfqKEa81FGcyyYI/0ZkEBAuSCq5njHitoTiTSRb8ic4kIFiQVHA9Y8RrDZb7M/REqHaTCdck26kFGZFjP5TSMhv1WkMta6nNluFiID34WpHCPTLLyKJ8NT1TiFYy1TY4eTPLSFoIFhVqV6uhyszAH0qtSOEeCQjCkhYssP7sJm91vkJvneUD+DUoSAAQrWRQWfiMNxW6UQn1rExm+QirkYAgfCYUKnVvyCwfYTUSEMRpzOqq8UVCPW9X4vpyJW8orRURgUFmGQkA6poaKamuoaSmmokDBrBs106qGxqoamigurGB6oYGqhsbqWpooK6piYbmZhqam6hvbnb83PL7obfOJP+d0yc4pF7+FQOv2kR4WBjhKowwpYgIO/XdFh6OLSKC6IgIosIjeP6a6/jZB+8RHR5BbFQUcVFRxEZGEev4HhcVSYItmuSYGJJ79SLBFk1YayRx8HYWja9n4cgsH+ELMstIdKmxuZnCqiqOVJSTX1FOfkUF+RXlHKuspKSmmpKaaqoaGto9415+9fEHbb+FK9WuIo5yVNrhRIVHEBdlwxYRTlR4OLbwCKb+VynqZx8RphR/nHkRD366CqUUCrDr4TRrTbPdTrPW2LWmyW6n2W6nobmZuqYm6pubqG6sBeCbwkLqmpraAlJXly4RYWH0iYkhOaYXyTG96Bcby0VR92LDeR+9OxVuV338RlTY3szykWnJwhekhRBETtbVsr+sjP1lpW3fD5woo7CqkuZ273OYUvSPi2dAfDz9YmPp2yuWL18exvvPpJ+2zwcebOa/F4ahOl19u8ObLKmdZxlpralpbKS6sbXV0kh5XR2ltTWU1tR0+H68pobi6mr+kPWfOCu21vBixTLSExLJSExkUEISGYmJpCckkmCztW23Zk0YOA1DiunT7Z69MANIy0J0RVoIIUZrzZGKcnKLisgtLiS3uJh9Zcc5XnOqgoiOiOCM3n2YOGAAGQlJpCckkJ6QyKCERNLi4ogMD++402nA0y0/dqzIO23XA95kSe08bqBaWylRUfSLdW8fGzYscjpAW6P7Ulpby7bCQsrr6zr8LaVXL4b07kN27z5MD08lUhee9nyz+/i9bblI60K4IgEhAJyorWXTsXy+KSp0BIGitoosKiyc4SkpTM/MYmifZIb0TmZon2QGJiSc1qfub2avI8jO/qPTK+lJIx/j8gtbKsCK+jqOlJdzuKKcw+UnyTtxgrwTZazcv5e86BnMTV+GLayx7flN2kZx2H/AkcOMSOlL75gYv78ub2YnWWHtg7AuCQgW0PmKLStrESVhs/j4wH5WfXeAb4+XAC395MOTU7j0jKGMTU1jbL9UhiWnENXuar+oaAl5ux7ggBdXf1a//4G73OmjT7BFM7pfNKP7pZ72/LLaO/n20GRqi/+HMHshVc3JvFN8OatKooE3Wo4RG8e41FTOTc/g3PRBDE9O8Xkg9iYHka/HRURgkzEEkznrD26wR/Fc/vVsKp/EWQMGMjUjk3MGpjO2Xyq2CNcx3Cp9y2atMvbXcUtqqvn2eAnfHi9hd0kJWwuOcbiiHIA+0TGcmz6Ic9MHMWVQBllJvT0af+mKN++zVcdFhHHkFpp+ZmQf7Lr1GTQ1Hjnt8eaw/kw4az99Yno5eZZzZtwG0lkl3JPBZCMrcTNv9Xm0ooIN+YfZkH+EDUcOU1hdxYmVkxl1Yy7TM7OZPjiLKYMyiI2KMuR4nn4G5VahwU8Cgh8ZcRVe3dDABwf28e9dO/mPPjc7nQnjyRWbGVd/zirhnlTMRlbiVrn3s9aag+Unye7dm7veXcH6w4eoamwgKiycswemMz0zixlZ2WQl9fZ72azSihS+I/dU9iNv8s8cKS/ngU8/5pzFT/Krjz+goKqSxrA0p9t6MpPFzJWvvlhlbOXjdkUp1VbZ//Pyq9g87ycsufZGbh+fQ2FVJX/4fA0zX3yWi156jv/bsJ7vTp5wuS+jX4cZNwKS+zYHDmkh9JAnV+GV9fX8Y/OXPPf1VlBw5bAR3DR6DJP6D6S4+BXDrtj8dfW3YIHzPEXz55+qoLv6WHX3fE9ZoYXgzms7Ul7O6oN5fHhgH18ezceuNVMGZfC9MeOYlX1Gh0kCVnhN3pAWif9Jl5Ef9aQPttluZ9muHfx5w3pKa2u4bsQo7psylbS4+A7bGTkm4e855tJl5Jo75SmuruKNXTt4dUcuRysrSOnVixtHjWHO2PEMiE8w5TUZ+RmSMQv/k4DgR+5e8Ww4cpg/fL6G3cdLmNh/AL+/YAbjU513D/WE1e4TYKWAEAjnxpVmu521hw/ySu43/PsfaZz4YPJp23jbgnKH0Vf0MqvJ/2QMwY+664M9UVvLzz98jzlvvUFFfT1PzL6C12+4xZBgANZLKd26ZsHTvnwj1zyYGQyc9ZP35LWFh4UxIzObp6+8ltzXRvPwZ6sZ/Y/HAbjjrX+z7vAh5s/3/cWb0fdokIyugUVaCAbKLS5i3jvLKa2t4SeTzuHHk87uct2AJ6zWLeJMIJTRSL7qJy+vqyMpJpqznv4nx2tqyEntz+/On8akAQONKLZTRl/RyxiC/0kLwQI+yTvALcteJSIsjLdu+h4/P3fKacHA0ytYK86kEaf46s5nidHRzJ8Pn8/9D/4wYxbHqiq4admr3PfRSspqa7rfQSfuzPYx+orejFlNwnPSQjDAC99s5b/XrmFMv1SevuIa+sY6z75mxJVzIFx9W60v39dcXVVrrZgxw7h+8prGRv6x6Uue2rqJhCgbv79gBlcPH+HWSmh3r9Tlij7wSQvBJM12Ow+vXc3Cz1YzK2sIS6+7yWUwCCWBEgyMKqerq+eiImP7yXtFRnLflKmsuOX7ZCQm8cuP3ufOt98k35E2oyvutmLkij60SUDwUH1TEz95fwXPb9vKnTln8vfLriQmMvK07Yzu7gmWxHNWYNQAfXb2IsLCOqYYCQvrxTPPLDLmAJ2MSOnLGzfewvxpM9hScJRLXn6eZ7/eQlet/Z5kSE1NncPkyQeZPt3O5MkHJRiEEAkIHlr0+Ro+zjvA/GkzePCCGYSHOT+VCxa0dPG0/q+2/uzNeEIgclXuQH097bW/qtZaUVg4mIcffopPPpnjs/Ge8LAw7hh/Jh9+fy7npmfwh8/X8OP3VnS6890pMttHuEPGENzUfrGOPbw/T383jXHZ/8lvp05zex+B0P/vK65eu7/PSVcriVv/bhR/vTatNc9u28qf1n3GyJS+LL7qutO6LmVsIHTIGIKPtf4ztay41IQ1H+MHg/7N7UO6vyFJe9LdY76uWmxddSFZuSWjlOKHEybyryuu4cCJMm54Yyl5J8o6bCNjA8IdEhDc4GxALlI1cPjggz3aj5UrFV9wNX4yfXrgTaP1ZLzB3xcAF2Zl88p1N1Hd0MCNbyzl64JjHf4uYwOiO4YEBKXUbKXUHqXUfqXU/U7+PlcpVaKU2ub4+pERx/UXb25ZaBVm3bDG2dX4mjXGjqt4qn0yPl8EJzPO+fi0/iy76VYSbNF8/6032HzsqM+PKdlMg4fXAUEpFQ78HbgUGAXcqpQa5WTT17TWOY6vZ7w9rj8ZNSBn5j+O1VJeWEHreglXwSlQFwRmJvVm0t7bSIuL54cr3mJ3SbHPjtW5O7X1Hs0SFAKTES2Es4H9Wus8rXUD8CpwtQH7tYzs7EU0aVuHx8LCepGd7f60wlD/x3HVfWLlcRWjZ4j505//GMWL19xAXFQkd7z9bw52cc8Fb/hqlbYwhxEBYSDQ/h6Q+Y7HOrteKbVdKbVMKTXI2Y6UUvOUUpuVUptLSkoMKJoxCvWFLD5yHfWk4umAnKf/ON5UPt5c4Rpd6QXCtFMrBydPDExI4MVrbsBu19y+fBmlNT1Pd9GdYOhOFaf4a1D5HSBTaz0O+Bh4wdlGWuuntNaTtNaT+vbt66eidU1rzR/Xfcb++vM5b8phjwfkPP3H8aarx5sr3FDsYurqvARCsHB2AXBGcjKT9t5GcXU1//XBuzTbjU05LesbgosRAeEo0P6KP93xWButdanWut7x6zPARAOO6xe5xUVsOnaUu886hzgvbpAu/ziBzUotGVdcXQA8+ed4Hp4+kw35R3hp+zZDjtPK1SrtnnSnCuswIiBsAoYqpbKUUlHALcCK9hsopfq3+/UqYLcBx/WLV3dsJyYigutGjvZqPz35x/HFYKY7V7iBOogqunfjqDFMG5zFo1987lbuo660bz3K+obgYshKZaXUZcBfgHDgWa31IqXUw8BmrfUKpdT/0BIImoAy4Mda62+72qcVVipXNTRw7uInuXzocB6ZdYnX+/Pk1oRmrW4O5VXVwcBZxtmjlRXMfvl5JqQN4IVrrncrS6oz8tmwNrmFpo8s/3Y3v/zofV674WbOGpBuShkkIAgjvbx9Gw+t+YT/nXUJN4wa4/bzukr5IS1Ia5HUFT7ycd5+0mLjmNjfd3eo6o5Zg5lWHUSVysc73xs7nrMGDOSP6z6jor7O7ecF8hRc4T4JCC5ordlScJRz0gcR5mHT2ghm/cNZ9R89FGc/GSlMKR66YAYn6+p4eqt1kkcKa5CA4MKxykqKq6s5s/8As4sihKFG90vliqHDeW7bVkpqqnv8fKu2HoX3JCC4sKWgZebsmWn9u9lS+JrMfjLeLyafR31TE//Y9GWPn+uP8y75kcwhAcGFrwsL6BUZyfAUayyQszJfVxDSf228rKTe3DhqDK/kfsPRigqzi9NBqKd5MZMEBBf2lpYyrE8KES7uhCZOkX79wHTP2edi15qXcr1frGYkyY9kHqntXDhScZKMpESv9yNXscaS/mvjDIhPYGbWEP69awdNBqe08IbkRzKPBAQnmux2CiorGZTgfUAI1qtns/r1JcAa67qRoyitrWX94UNmF6WNpHkxT0gFBHcHqgoqK2nW2pCAYDVGVajSrx8cpg3OIsFmY8XeLhMH+JXkRzJPyASEngxUFVRVAi1Nak9YeVZMsLZYhGdsERHMHjKUjw/sp7G52eziAJIfyUwhExB6MlBVVfoG/zviDzTlZXk05S3Urp6lXz+wTc/MpqqxgW1FBWYXpY3c/9kcIRMQ3B2oKipagir7HSlRJwmWKW++brEEa6ALFt29P1MGtazGX+ejcQRZUxA4QiYguDtQlZf3AIqOOV68mfJmhavnUGuxiI666yZMsEUzPjWNzw8ZHxBkTUFgCZmA4O5AldFT3qTSFYFgasZgthcXUl7nfsI7d8iagsASMgHB3YGqYJ/yZoUWi/C9nnYTnj0wHbvWbC8uNLQcsqYgsESYXQB/Sk2d0+3gVHb2Inbu/hFh7bqNgmnKm7RYQkP7G+S4c2+LMX1TAdhRXMT5GZmGlcNmy3B0F53+uLCekGkhuCs1dQ4lMQ9wvCGJQJryJhW98EZidDSDE5PILSoydL+ypiCwSEBwoi76Mn797e8Zd06VaVPeelrBy/oC4Yq73YRj+6WSW2xsQJA1BYElpLqM3BUV3nJa6pvMW6izcKFc9QtjuPs5GtW3H+/u20NFfT0JNpthx3enq1ZYg7QQnEi0RQNQ3oNbDJrByiuiReDJTOoNwOHykyaXRJhFAoITSdGOgGDwFLzu9LSCt8r6AglAwWFwUhIAh05KQAhVEhCcaA0IJ/3cQrBKBd9TMn4RuNp/tjIcyRwPSQshZElAcKI1IJyorTW5JO6T9QXCE+2DeWxUFCm9eklACGESEJxI6RWL4lTWUzP0tII3o5tIxi+CT2psHCU11WYXQ5hEAoITUeHhpMbGcazSvIBg9Yo1ULu3RNfBPDmmF2UB1DIWxpKA4MLAhATL3XxcCCN0Fcz7xMRQVlvT1dNFEJOA4MKA+ASOVUpAcIeMXwSPPkHaQpAU3O6RgOBCRmIiRysraLDIXaSsTLqJAlfnYJ4YbaOmsZEmu92cAnXB00pdUnC7TwKCC2f0SaZZaw6ePGF2UYTwmc7B3OZYpW+1CyFvKnVJwe0+CQguDO2TDMD+slKTSyKE/9giwgGob2oyuSQdeVOpSwpu90lAcCG7d28UsE8CggghrS2E+mZrBQRvKvVgv8eJkSQguBAdEUlGYhJ7jh8/7W8yQCWCVVR4awvBWl1G3lTqkoLbfRIQujC6bz92lhR3eCyQBqg8GeyVAeLQ1uyYixoepkwuSUfeVOqSgtt9EhC6MDY1lSMV5R1SWATSAJUnOYYkL1Foa51dFBFmrarB20o9NXUOkycfZPp0u2n3OAkE1nrXLWZcvzSADjcNMWKASq7CRU/56zPT6JhdFBEW7p8DdqN992xe3gNkZy+SSt2HDAkISqnZSqk9Sqn9Sqn7nfzdppR6zfH3L5VSmUYc19fGpqYRphRbCo62PWbEAJUvr8I9yTEkeYmsz18tt9YWQqQFWgiB1D0bLLx+15VS4cDfgUuBUcCtSqlRnTb7IXBCa30G8BjwiLfH9Ye4qCjG9ktl/eFTNwm3+gCVJzmGPM1LJAEj+NQ2NQIQHWH+zRQDqXs2WBhxGXA2sF9rnae1bgBeBa7utM3VwAuOn5cBM5VS1hq1cuGCwZlsKyrkZF3LOIKnfZnBeBUu4w2+5evPjLPZcuV1dURHRGCzQECQ9QP+Z0RAGAgcafd7vuMxp9torZuAciC5846UUvOUUpuVUptLSkoMKJr3pg/Owq4169q1EjwZoDIjO6gnOYYkL5F1+PIz46o7plfDyrZbyJpN1g/4n/kdhe1orZ/SWk/SWk/q27ev2cUBYFxqGknR0Xx26KDZRekxX0w7DcaWTihy1R0zVD1Hos1mUqk6snr3bDAyIiAcBQa1+z3d8ZjTbZRSEUAiEBBLgMPDwjg/I5M1B7+j2aCEX1a+Cu9u0Z3cB8EcRn9mXHW79FIzHKdoAAAXUklEQVTHSYy2RgtB1g/4nxEdhZuAoUqpLFoq/luA73XaZgVwB7ABuAH4VOvWKsX6Ls4+g3f2fsuWgmOcPTC9x88vKlpCXt4D1NcfxmbL4Mc/XgRY70Pd2o3QeuXY2o0AyD+hyYwOuDZbhqO7qKPy5t6kxsUZezAvpKbOkc+eH3ndQnCMCdwDfAjsBl7XWu9USj2slLrKsdliIFkptR/4JXDa1FQrGxO7kUdHLKJ6X0aPU1UE0tS5ns7qsHJLR3TNVXfMvwsuZUBcvM+PL+lfrMmQqQRa6/eB9zs99lC7n+uAG404lr8VFS3h0IGfkBzl2VVzV5Ws1a58ejqrQ7qJAlfrZ699y7XvwPms31bGzLG+DQjSErUuSw0qW5G3c6EDaeqczOoILZ1ny9VFXwZAmo9bCLK+wLokIHTD2wo9kCpZmdUR2g6dPAm03C3QlwLpIinUSEDohrcVutGVrC/7XmVWR2jLO1mGArKSevv0OIF0kRRqzF+OaHHZ2Ys69HcCaBXjdoXurK82O3uRR5WsP/peZVZH6FryeDIDZyUQExnp0+M4+5+Slqg1SEDoRucKvawxif36B8zoQaVpVCUbSAPUIvB8uWQYc2/M9flxjLxIEsaSgOCG9hX6Q6tX8caunfznBXV+X8Ajfa/uWbBAZkD1VEuW0zCG9D4to4xPSEvUmmQMoYduHj2W+uYmlu/Z5fdjS9+reyTpnvtaU5FEhrdUBQ9Omy6pSEKYBIQeGt0vlbH9Unl1Ry7+XmwdCrOApCLqnpHnqDUVybJdOwHYV1rqdioSea+CjwQED9w6Zhx7So+zrbDAr8f19SwgK/yDe3p1H0pJ93zRAsotKgR6NsNIWmLBR1k1pdCkSZP05s2bzS6GU1UNDUxe/CSzzxjGoxfNBk7PVxSIg2RKnUpa1xVf9tG7WwZf78PKfPH6bnj9FXYvG8fO18eYVo5g+B+yAqXUFq31JE+eKy0ED8RFRXHtiFG8s/dbSmqqAypfkRGMvjIMpat7T/nyHNU2NpJbXMRtPyszrRyh9j9kVRIQPHTnhIk02e38a/OmgF6Kb4XK2OiU2mYm3fPVefNl2vGthcdotNs5x41Mvr4qRyD/DwUTCQgeykrqzbUjRrEk95uAng7q7j+4FQKHu8wsUyD2q391NJ+TK6cwqX/nGx36TyD/DwUTCQhd6C5NxH+dPZlmbadWO7+7m5nTQY1OceGvG+NISu3uGX2OvszP58QHk4nv4Z3SjCyHTKm2BgkILrjTpzkoMZEbR41hSf5FKBXT4flmTgf1tD/WCpWxFVsc3fF368nI/VY3NHg8W87IcoTClOpAIAHBBXf7NH9+zhS+qTqbL2p/bImkcAsWeN4f6+4/uCeBIxArencF6m1FFyyAOFsUe376c8DcbkBJrGgNMu3UhTVrwgBn50YxfXrHeyv/7auN/N/G9bx6/c0e3WLTSErB6tXul91fgn0qaKtAe52/WfUhK/fvJffHPw2ocgvXZNqpD/SkT/OHEyaSFhvHH9d9ht0H/1U9HQ+Q/ljzWKHbzV31TU18sH8fs7KGmF0UYRESEFzoSZ9mTGQk906ZyvaiQlbs2W1oOdwZD+jch/3gg4uoqzO/PzaQZiYZJZBe2yff5VHZUM/Vw0cGVCATviNdRl3oycpJu9Zc//orHK2sYNVtPyChhzM2XNmwIdMRDDqy2QYzefLB0x5v7bKw2qrPQOtKCQVz3nydQ+Un+eyOHxEeJteGwcKbLiNJf92FnqToDVOKhdNncu1rS/jLxvU8NO1CQ8rg6fxsSS8surKvtJQN+Ue4b/JUCQaijXwSDDQuNY3vjR3Pi9u3sbuk2JB99nQ8wKpNf6uWK1S9nLuNqLBwbh491uyiCAuRgGCw+yZPJckWzYOrV9Fs935GT0/nZ1u1D9uq5QpFVQ0NvLV7F5cNHUZyr17dP0GEDAkIBkuMjub3F0xna2EBj3+1wev9Ber8bKNXSgvjvJL7DVWNDdwxfoLfjy2fC2uTMQQfuGbEKL7IP8wTX21kQtoApmdmebW/QBsPaJ0Z1bo4rnVmFBBQryMY1TU18szXmzlvUAbj0/r79djyubA+aSH4yMPTZzIipS+//Oh9jlZUmF0cv+pupbR0H5nn9Z07OF5Tw91nnev3Y0tGU+uTgOAj0RGR/OOyK2my27l75TvUNzWZXSS/6W5mlFEZQSWw9ExDczP/2rKJif0HuJXq2miS0dT6JCD4UGZSbx69aDbbiwr552cPsGHDYJ/3nVqhj9ZfK6X9nWrarABk1Hv6xq4dFFRVcvdZ56JaVwv6kaygtz4JCD52yZChPDihgpHqMceVkO/uBmWVu045mxnV3NyLBx9cFNCrls2414FR72llfT1/2fgFZw0YyLTBmT4pa3cko6n1SUDwgxERz2MLa+zwmC/6Tq3SR+tsZtSYMU+xatUcrzOChlo6DKPe06e2bqK0tobfnT/dlNYBBO6MuVAis4z8oL7+iIvHje07tVIfbfuZUa1pNHbvvg2bLYOZMxcBnlUCCxacqvz9kQ5jwYKOLYPWunT+fP8EISPe04LKSp7ZuoWrho9gfGqaUUXzSKDNmAs10kLwA3/1nVqxj9ZZl8dvfxs4N083+14H3r6nWmsWfPYJGs19k6caWTQRhCQg+IGzvtMGexQxfe/3+XHM7qN11uURHm5MN1YopMPw9j1d/PUWPs47wK+mnE96QqIviiiCiAQEP+jcdxoemc6bJXP4wafNfFNU6LPjWKGP1pfdWP4eNzAjAHnznn51NJ9H1q/lkiFD+UHOmb4vrAh4XqW/Vkr1AV4DMoGDwE1a6xNOtmsGch2/HtZaX9Xdvq2Q/tqXDpef5La3llFWW8PTV17LuemDzC6ST/Q0fbcwRkl1NVcsfYnYqCjevnkO8QalYxfWZ+Yd0+4HPtFaDwU+cfzuTK3WOsfx1W0wCAUZiUm8dsPNDIhP4M633+ST7w6YXSSfsGI3VrBrstv56cp3qWqo55+XXyXBQLjN24BwNfCC4+cXgGu83F9ISYuLZ+n1NzEsOZm73n2bl7dvM7tIhrNiNxYE5zTVlgFwzUOrV/HVsXwWXXgRw5NTzC6WJRZLCvd422V0Umud5PhZASdaf++0XROwDWgC/qS1Xu5if/OAeQAZGRkTDx06vashGFU1NPCzD95j9cE8bhuXw++mTsMWITOCfSkQ7+DWfsqtM0rBE19u5P82rufus87hXi9nFXV3PHd0TmgHLS1EK1wUBCtvuoy6DQhKqVWAs8nLDwAvtA8ASqkTWuveTvYxUGt9VCmVDXwKzNRad9lHEuxjCJ012+08sn4tz3y9hdF9+/HX2ZeT3buP2cUKWoEYELors1KQ9df/x3UjRvHoRbO9XoBmxDmSMST/8+kYgtZ6ltZ6jJOvt4EipVR/RyH6A05vE6a1Pur4ngesAfyfiN3iwsPC+N3503n6ims4WlnBVa++zFu7d5ldrKASjKucO7+m7352L//vkktZuNCc1cjQsYvIWTAASWhnVd6OIawA7nD8fAfwducNlFK9lVI2x88pwHmA1HQuzMwewnu33s7ovv249+OV/PzD9zhRW2t2sYKC2YvMXJWpu793FcTmz9e8sO1rhjz+fwBU1NV79Zq8DZqdFyK6IgntrMnbMYRk4HUgAzhEy7TTMqXUJOAurfWPlFJTgH8BdloC0F+01ou723eodRl11mS3849NX/K3TRtJio7mDzNmcfGQoWYXy+da01zU1x/GZssgO3uRT/qaZ81awn//t++PA12/pp50y3Tetr6piflrPuH1XTu4MDObxVdfa2g3mCddRq66iNqTMQTf8ukYgllCPSC02lVSzK8//oBdx0u4OPsMfjt1GoOTThu3Dwr+GoAsKlrCjh3zCA/3/UBnd6/J04BQXF3FT95bwdbCAu4+6xx+ce55PLxQGdra8SQgrFkThuuWgfJ58BXmrkMQPjaqbz/eunkO902eyrojh7jk5ef50/q1VNbXm100w/krW2te3gMdgoGr4xhRubp6TatXP9DjbpnWldLfFBZw9atL2H28hH9eoJnC91n7WTiXXGLslE5PVma7zr00mOnT7UyefFCCgYVJCyGAFFVV8ecN6/j37p0kx/Til5PP44aRo4kMDze7aIZwfXWpmD7d7vfjGDHLprtj9eQYWmuW7d7Jg6tX0S82lr+c10RVwX2WmtIp00zNJy2EEJEaF8ejF81m+c1zyExK4oFPP+bil5/nzd07aWxuNrt4XgvGrLBGHWv38RK+/9Yb/GbVh0zsP4DlN8+h/vgjlrj/RXtWXYgo3CMBIQCNS03j9Rtu4ekrryEuKor7Pv6A6S8s5l9bvqK8rs5nx/X1ilN/pbno6jhGT03t7jV11y1TWlPDA59+zJVLX2L38RIWTLuQF6+5gT4xvSx1/4v2UlPnMHnyQekiCkDSZRTgtNZ8ejCPZ7/eyob8w/SKjOT6kaO5Y/wEQxe2+XPA1x+zjNw5jlGL1zx5TQ3Nzby0fRuPf7mBmsYGbhuXw3+dM5mk6Ji2bWTRl3BGZhkJAHaXFPPstq28s+dbGu3NzMjM5s4JZzIlPcPrVauhWPmYsZq5NcD/z7rPyDtxggsyMvn9BdM5o0/yadtKf71wxpuAIAlzgsjIvv149KLZ/HrK+bycu41Xcr/htreWMTA+gUvPGMplQ4czPjXNo+Bg1e4JX/Ln/Q8q6ut469tdLM3dzt6yUrKSevPMldcyIzPL5fvVWun7o0UlQoO0EIJYfVMTK/fv5Z29e1h3+CCNdjsD4uO59IxhXHbGMHLS+rsdHEKxheBrWmu2FxXyyo7tvLP3W+qamhjbL5Xvj8vh6uEjiQqS2WPCv6TLSHSror6OVXkHeH/fXtYdPkSDvZm02DimZWYxbXAWUwZlkNBF3nzpnjBOcXUVH+zfxxu7drCzpJhekZFcPXwkt44Zx5h+qWYXTwQ4CQiiRyrq6/kk7wAf5e1n/ZFDVDU0EBEWxplpA5iWmcm0wVmMTOl7WuvBXwO+wehoRQUfHNjHB/v3srXgGBoYmdKXW8eM4+rhI+UmNsIwEhCExxqbm/m6sIA1B79j7aHv2HW8BIDkmF5MGjCQM/v3Z1y/NMb0SyU2Ksrk0gaO+qYmdpYUsyH/MB8d2E9ucRHQEgRmnzGU2UOGMTT59IFiIbwlAUEYpri6is8OHWRj/hE2Hcsnv6ICAAWc0SeZcalpjO7bj6HJyQxLTiElppfXM5gCndaao5UVfF1YwNcFx/i6sIBdJcU02ltWPY9LTWP2kKHMPmMomUmn3S5ECENJQBA+c7ymhu1FhS1fxYXkFhVS2i4dd5/omLbgMLRPMlm9ezM4MYn+cfGEhwXfusfK+nr2l5Wyt6yU/WWl7CstZdfxYo7XtIytREdEMK5fGjn9+3NmWn8m9B9A316xJpdauvtCiQQE4Tdaa47X1LCn9Dj7ykrZW3qcvaXH2VdaSlVjQ9t2kWFhDIhPYHBiEhmJiWQkJpEWF0e/2DhSY+PoFxtLTGSkia/EObvWFFdXcbSygqMVFRyrrORoZQVHysvZV1ZKQVVl27a28AjO6NOH4ckp5KT1Z0Jaf4Ylp1gut5RMCAgtEhCE6bTWHKuq5NDJkxwpP8mh8nIOl5/kcEXL9won2VkTbDZSY+NI6RVLUnQ0iTYbidHRJNqiHd9txEfZsEVEEB0RgS0iAlt4OFHh4djCI4hwtEC0I3lc241v0BwvfpXi/Pk0NR4lLGIg4X1+RWOvK6lpbKSivo6y2lpO1NVyoraWstbvtbUUVlW2dfW0SoqOJj0+gSF9khnaJ5lhyckM7ZNCekJCQLSCZMpwaJGFacJ0SikGxicwMD4BBp2euK28ro6i6iqKqqsorq6mqKqK4uoqiqqrKamuYm9pFeX1dVTU1dNg9y5R3zlJW5ibvgxbWCMA9qZ8agvv4/n8jXx5cmLbdr0iI+kdHUPvmBj6RMeQmdSb/nHxDIiPZ2BCQtvr6W4w3erdMaG4qFB4RgKC8IvE6Jar/mHJKV1up7WmrqmJ8vo6yuvrqayvp66pifrmJuqbmqhraqKhuZmG5mbsWrcllm4d1lYKBpb/mQh7Y4f92sIauSt7LQ+N+CuJNhu9o2MM6bLq3B1TX3+IPXvmAVgmKNhsGS5aCHIbS9GRBARhKUopYiIjiYmMJC0u3qN9rFlT5PRx3XSMkSl9vSneabq6qY9VAkJ29iKnYwhGZ5EVgc/6HaBC9JA/73cQCN0xco8C4S5pIYig488r4kDpjklNnSMBQHRLWggi6PjzithfN/URwh+khSCCkr+uiCUFtQgmEhCE8JJ0x4hgIV1GQgghAAkIQgghHCQgCCGEACQgCCGEcJCAIIQQApCAIIQQwkECghBCCEACghBCCAcJCEIIIQAJCEIIIRwkIAghhAAkIAghhHDwKiAopW5USu1UStmVUi5v6qyUmq2U2qOU2q+Uut+bYwohhPANb1sIO4DrgLWuNlBKhQN/By4FRgG3KqVGeXlcIYQQBvMq/bXWeje03Ae3C2cD+7XWeY5tXwWuBnZ5c2whhBDG8sf9EAYCR9r9ng+c42xDpdQ8YJ7j13ql1A4fly1QpADHzS6ERci5OEXOxSlyLk4Z7ukTuw0ISqlVQJqTPz2gtX7b0wM7o7V+CnjKcdzNWmuX4xKhRM7FKXIuTpFzcYqci1OUUps9fW63AUFrPcvTnTscBQa1+z3d8ZgQQggL8ce0003AUKVUllIqCrgFWOGH4wohhOgBb6edXquUygcmA+8ppT50PD5AKfU+gNa6CbgH+BDYDbyutd7pxu6f8qZsQUbOxSlyLk6Rc3GKnItTPD4XSmttZEGEEEIEKFmpLIQQApCAIIQQwsEyAUHSYJyilOqjlPpYKbXP8b23i+2alVLbHF9BNVDf3fuslLIppV5z/P1LpVSm/0vpH26ci7lKqZJ2n4UfmVFOX1NKPauUKna1Pkm1eNxxnrYrpc70dxn9xY1zMV0pVd7uM/GQWzvWWlviCxhJy4KKNcAkF9uEAweAbCAK+AYYZXbZfXAu/he43/Hz/cAjLrarMrusPnr93b7PwE+AJx0/3wK8Zna5TTwXc4G/mV1WP5yLC4AzgR0u/n4ZsBJQwLnAl2aX2cRzMR14t6f7tUwLQWu9W2u9p5vN2tJgaK0bgNY0GMHmauAFx88vANeYWBYzuPM+tz9Hy4CZqpscKgEqVD7z3dJarwXKutjkauBF3WIjkKSU6u+f0vmXG+fCI5YJCG5ylgZjoEll8aVUrXWB4+dCINXFdtFKqc1KqY1KqWAKGu68z23b6JapzeVAsl9K51/ufuavd3STLFNKDXLy91AQKvWDuyYrpb5RSq1USo125wn+yGXUxp9pMKyuq3PR/hettVZKuZobPFhrfVQplQ18qpTK1VofMLqswvLeAZZqreuVUv9JS8vpQpPLJMy1lZb6oUopdRmwHBja3ZP8GhC0pMFo09W5UEoVKaX6a60LHE3eYhf7OOr4nqeUWgNMoKW/OdC58z63bpOvlIoAEoFS/xTPr7o9F1rr9q/7GVrGoEJR0NQP3tJaV7T7+X2l1D+UUila6y4TAAZal1GopMFYAdzh+PkO4LTWk1Kqt1LK5vg5BTiP4Ekp7s773P4c3QB8qh2jaUGm23PRqZ/8KloyAoSiFcDtjtlG5wLl7bpeQ4pSKq11TE0pdTYtdX33F0xmj5a3GxW/lpY+v3qgCPjQ8fgA4P12210G7KXlSvgBs8vto3ORDHwC7ANWAX0cj08CnnH8PAXIpWXWSS7wQ7PLbfA5OO19Bh4GrnL8HA28AewHvgKyzS6ziefif4Cdjs/CamCE2WX20XlYChQAjY664ofAXcBdjr8rWm7GdcDxP+F0tmIwfLlxLu5p95nYCExxZ7+SukIIIQQQeF1GQgghfEQCghBCCEACghBCCAcJCEIIIQAJCEIIIRwkIAghhAAkIAghhHD4/+A6zvTVcV0vAAAAAElFTkSuQmCC\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"create_plot_for_lambda(X, y, 10)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"#### Underfitting$^2$\\n\",\n    \"This is what model trained with an extremely high value of $\\\\lambda$ looks like:\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 62,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"Optimization terminated successfully.\\n\",\n      \"         Current function value: 0.687913\\n\",\n      \"         Iterations: 10\\n\",\n      \"         Function evaluations: 23\\n\",\n      \"         Gradient evaluations: 23\\n\",\n      \"Conjugate gradient found the following values for theta - first five values only: [ 0.00980668 -0.01412537  0.00377853 -0.042739   -0.01022205]\\n\"\n     ]\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"create_plot_for_lambda(X, y, 130)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Adjusted normal equation\\n\",\n    \"As you would have expected, the normal equation changes when you add normalization to your machine learning model. The adjusted version of the normal equation: \\n\",\n    \"\\n\",\n    \"$$\\\\theta=(X^TX+\\\\lambda\\\\begin{bmatrix} 0&\\\\dotsi&\\\\dotsi&\\\\dotsi &0\\\\\\\\\\\\vdots &1&0& 0 & \\\\vdots&\\\\\\\\\\\\vdots&0&1 &0 & \\\\vdots\\\\\\\\\\\\vdots&0&0&1&\\\\vdots\\\\\\\\0&\\\\dotsi&\\\\dotsi&\\\\dotsi&1 \\\\end{bmatrix})^{-1}X^Ty$$\\n\",\n    \"\\n\",\n    \"If $m < n$, $X$ is [non-invertable](https://www.quora.com/What-is-a-non-invertible-matrix-What-are-some-examples).\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 60,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"array([ 0.94416708,  0.2315894 ,  0.41142826, -0.7380916 , -0.50116657,\\n\",\n       \"       -0.69193639,  0.1003575 , -0.10718673, -0.06667559, -0.05556887,\\n\",\n       \"       -0.45471969,  0.09321721, -0.23956536, -0.07088082, -0.40279421,\\n\",\n       \"        0.04618662, -0.01432296,  0.04153635, -0.10356044, -0.02654812,\\n\",\n       \"        0.05619122, -0.18296629,  0.12363998, -0.11445861,  0.06788982,\\n\",\n       \"       -0.10602358,  0.04149463, -0.05781815])\"\n      ]\n     },\n     \"execution_count\": 60,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"L = np.eye(n)\\n\",\n    \"L[0] = 0\\n\",\n    \"_lambda = 1\\n\",\n    \"theta = np.linalg.inv(X.T @ X + _lambda * L)@X.T@y\\n\",\n    \"theta\"\n   ]\n  }\n ],\n \"metadata\": {\n  \"kernelspec\": {\n   \"display_name\": \"Python 3\",\n   \"language\": \"python\",\n   \"name\": \"python3\"\n  },\n  \"language_info\": {\n   \"codemirror_mode\": {\n    \"name\": \"ipython\",\n    \"version\": 3\n   },\n   \"file_extension\": \".py\",\n   \"mimetype\": \"text/x-python\",\n   \"name\": \"python\",\n   \"nbconvert_exporter\": \"python\",\n   \"pygments_lexer\": \"ipython3\",\n   \"version\": \"3.7.1\"\n  }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n"
  },
  {
    "path": "ex2/ex2data1.txt",
    "content": "34.62365962451697,78.0246928153624,0\n30.28671076822607,43.89499752400101,0\n35.84740876993872,72.90219802708364,0\n60.18259938620976,86.30855209546826,1\n79.0327360507101,75.3443764369103,1\n45.08327747668339,56.3163717815305,0\n61.10666453684766,96.51142588489624,1\n75.02474556738889,46.55401354116538,1\n76.09878670226257,87.42056971926803,1\n84.43281996120035,43.53339331072109,1\n95.86155507093572,38.22527805795094,0\n75.01365838958247,30.60326323428011,0\n82.30705337399482,76.48196330235604,1\n69.36458875970939,97.71869196188608,1\n39.53833914367223,76.03681085115882,0\n53.9710521485623,89.20735013750205,1\n69.07014406283025,52.74046973016765,1\n67.94685547711617,46.67857410673128,0\n70.66150955499435,92.92713789364831,1\n76.97878372747498,47.57596364975532,1\n67.37202754570876,42.83843832029179,0\n89.67677575072079,65.79936592745237,1\n50.534788289883,48.85581152764205,0\n34.21206097786789,44.20952859866288,0\n77.9240914545704,68.9723599933059,1\n62.27101367004632,69.95445795447587,1\n80.1901807509566,44.82162893218353,1\n93.114388797442,38.80067033713209,0\n61.83020602312595,50.25610789244621,0\n38.78580379679423,64.99568095539578,0\n61.379289447425,72.80788731317097,1\n85.40451939411645,57.05198397627122,1\n52.10797973193984,63.12762376881715,0\n52.04540476831827,69.43286012045222,1\n40.23689373545111,71.16774802184875,0\n54.63510555424817,52.21388588061123,0\n33.91550010906887,98.86943574220611,0\n64.17698887494485,80.90806058670817,1\n74.78925295941542,41.57341522824434,0\n34.1836400264419,75.2377203360134,0\n83.90239366249155,56.30804621605327,1\n51.54772026906181,46.85629026349976,0\n94.44336776917852,65.56892160559052,1\n82.36875375713919,40.61825515970618,0\n51.04775177128865,45.82270145776001,0\n62.22267576120188,52.06099194836679,0\n77.19303492601364,70.45820000180959,1\n97.77159928000232,86.7278223300282,1\n62.07306379667647,96.76882412413983,1\n91.56497449807442,88.69629254546599,1\n79.94481794066932,74.16311935043758,1\n99.2725269292572,60.99903099844988,1\n90.54671411399852,43.39060180650027,1\n34.52451385320009,60.39634245837173,0\n50.2864961189907,49.80453881323059,0\n49.58667721632031,59.80895099453265,0\n97.64563396007767,68.86157272420604,1\n32.57720016809309,95.59854761387875,0\n74.24869136721598,69.82457122657193,1\n71.79646205863379,78.45356224515052,1\n75.3956114656803,85.75993667331619,1\n35.28611281526193,47.02051394723416,0\n56.25381749711624,39.26147251058019,0\n30.05882244669796,49.59297386723685,0\n44.66826172480893,66.45008614558913,0\n66.56089447242954,41.09209807936973,0\n40.45755098375164,97.53518548909936,1\n49.07256321908844,51.88321182073966,0\n80.27957401466998,92.11606081344084,1\n66.74671856944039,60.99139402740988,1\n32.72283304060323,43.30717306430063,0\n64.0393204150601,78.03168802018232,1\n72.34649422579923,96.22759296761404,1\n60.45788573918959,73.09499809758037,1\n58.84095621726802,75.85844831279042,1\n99.82785779692128,72.36925193383885,1\n47.26426910848174,88.47586499559782,1\n50.45815980285988,75.80985952982456,1\n60.45555629271532,42.50840943572217,0\n82.22666157785568,42.71987853716458,0\n88.9138964166533,69.80378889835472,1\n94.83450672430196,45.69430680250754,1\n67.31925746917527,66.58935317747915,1\n57.23870631569862,59.51428198012956,1\n80.36675600171273,90.96014789746954,1\n68.46852178591112,85.59430710452014,1\n42.0754545384731,78.84478600148043,0\n75.47770200533905,90.42453899753964,1\n78.63542434898018,96.64742716885644,1\n52.34800398794107,60.76950525602592,0\n94.09433112516793,77.15910509073893,1\n90.44855097096364,87.50879176484702,1\n55.48216114069585,35.57070347228866,0\n74.49269241843041,84.84513684930135,1\n89.84580670720979,45.35828361091658,1\n83.48916274498238,48.38028579728175,1\n42.2617008099817,87.10385094025457,1\n99.31500880510394,68.77540947206617,1\n55.34001756003703,64.9319380069486,1\n74.77589300092767,89.52981289513276,1\n"
  },
  {
    "path": "ex2/ex2data2.txt",
    "content": "0.051267,0.69956,1\n-0.092742,0.68494,1\n-0.21371,0.69225,1\n-0.375,0.50219,1\n-0.51325,0.46564,1\n-0.52477,0.2098,1\n-0.39804,0.034357,1\n-0.30588,-0.19225,1\n0.016705,-0.40424,1\n0.13191,-0.51389,1\n0.38537,-0.56506,1\n0.52938,-0.5212,1\n0.63882,-0.24342,1\n0.73675,-0.18494,1\n0.54666,0.48757,1\n0.322,0.5826,1\n0.16647,0.53874,1\n-0.046659,0.81652,1\n-0.17339,0.69956,1\n-0.47869,0.63377,1\n-0.60541,0.59722,1\n-0.62846,0.33406,1\n-0.59389,0.005117,1\n-0.42108,-0.27266,1\n-0.11578,-0.39693,1\n0.20104,-0.60161,1\n0.46601,-0.53582,1\n0.67339,-0.53582,1\n-0.13882,0.54605,1\n-0.29435,0.77997,1\n-0.26555,0.96272,1\n-0.16187,0.8019,1\n-0.17339,0.64839,1\n-0.28283,0.47295,1\n-0.36348,0.31213,1\n-0.30012,0.027047,1\n-0.23675,-0.21418,1\n-0.06394,-0.18494,1\n0.062788,-0.16301,1\n0.22984,-0.41155,1\n0.2932,-0.2288,1\n0.48329,-0.18494,1\n0.64459,-0.14108,1\n0.46025,0.012427,1\n0.6273,0.15863,1\n0.57546,0.26827,1\n0.72523,0.44371,1\n0.22408,0.52412,1\n0.44297,0.67032,1\n0.322,0.69225,1\n0.13767,0.57529,1\n-0.0063364,0.39985,1\n-0.092742,0.55336,1\n-0.20795,0.35599,1\n-0.20795,0.17325,1\n-0.43836,0.21711,1\n-0.21947,-0.016813,1\n-0.13882,-0.27266,1\n0.18376,0.93348,0\n0.22408,0.77997,0\n0.29896,0.61915,0\n0.50634,0.75804,0\n0.61578,0.7288,0\n0.60426,0.59722,0\n0.76555,0.50219,0\n0.92684,0.3633,0\n0.82316,0.27558,0\n0.96141,0.085526,0\n0.93836,0.012427,0\n0.86348,-0.082602,0\n0.89804,-0.20687,0\n0.85196,-0.36769,0\n0.82892,-0.5212,0\n0.79435,-0.55775,0\n0.59274,-0.7405,0\n0.51786,-0.5943,0\n0.46601,-0.41886,0\n0.35081,-0.57968,0\n0.28744,-0.76974,0\n0.085829,-0.75512,0\n0.14919,-0.57968,0\n-0.13306,-0.4481,0\n-0.40956,-0.41155,0\n-0.39228,-0.25804,0\n-0.74366,-0.25804,0\n-0.69758,0.041667,0\n-0.75518,0.2902,0\n-0.69758,0.68494,0\n-0.4038,0.70687,0\n-0.38076,0.91886,0\n-0.50749,0.90424,0\n-0.54781,0.70687,0\n0.10311,0.77997,0\n0.057028,0.91886,0\n-0.10426,0.99196,0\n-0.081221,1.1089,0\n0.28744,1.087,0\n0.39689,0.82383,0\n0.63882,0.88962,0\n0.82316,0.66301,0\n0.67339,0.64108,0\n1.0709,0.10015,0\n-0.046659,-0.57968,0\n-0.23675,-0.63816,0\n-0.15035,-0.36769,0\n-0.49021,-0.3019,0\n-0.46717,-0.13377,0\n-0.28859,-0.060673,0\n-0.61118,-0.067982,0\n-0.66302,-0.21418,0\n-0.59965,-0.41886,0\n-0.72638,-0.082602,0\n-0.83007,0.31213,0\n-0.72062,0.53874,0\n-0.59389,0.49488,0\n-0.48445,0.99927,0\n-0.0063364,0.99927,0\n0.63265,-0.030612,0\n"
  },
  {
    "path": "ex3/PE3 - Multi-class Classification and Neural Networks (Exercises).ipynb",
    "content": "{\n \"cells\": [\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"# Multi-class Classification and Neural Networks\\n\",\n    \"\\n\",\n    \"Stanford CS229 - Machine Learning by Andrew Ng. Programming exercise 3.\\n\",\n    \"\\n\",\n    \"Please check out [the repository on GitHub](https://github.com/rickwierenga/CS229-Python/). If you spot any mistakes or inconcistencies, please create an issue. For questions you can find me on Twitter: [@rickwierenga](https://twitter.com/rickwierenga). Starring the project on GitHub means a ton to me!\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 1,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"import numpy as np\\n\",\n    \"import pandas as pd\\n\",\n    \"import matplotlib.pylab as plt\\n\",\n    \"from scipy.optimize import minimize\\n\",\n    \"%matplotlib inline\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Multi-class Classification\\n\",\n    \"\\n\",\n    \"---\\n\",\n    \"For this exercise, you will use logistic regression and neural networks to recognize handwritten digits (from 0 to 9). Automated handwritten digit recognition is widely used today - from recognizing zip codes (postal codes) on mail envelopes to recognizing amounts written on bank checks. This exercise will show you how the methods you’ve learned can be used for this classification task.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 2,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"# start by loading the data\\n\",\n    \"import scipy.io as sio\\n\",\n    \"\\n\",\n    \"data = sio.loadmat(\\\"ex3data1.mat\\\")\\n\",\n    \"X = data[\\\"X\\\"]\\n\",\n    \"y = data[\\\"y\\\"]\\n\",\n    \"y = y.reshape(len(y))\\n\",\n    \"\\n\",\n    \"m, n = X.shape\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Visualising the data\\n\",\n    \"Draw 100 random samples from the dataset.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 3,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"<matplotlib.image.AxesImage at 0x10e3af780>\"\n      ]\n     },\n     \"execution_count\": 3,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"import random\\n\",\n    \"from PIL import Image\\n\",\n    \"\\n\",\n    \"# get 100 random images from the dataset\\n\",\n    \"num_samples = 100\\n\",\n    \"samples = random.sample(list(X), num_samples)\\n\",\n    \"display_img = Image.new('RGB', (200, 200))\\n\",\n    \"\\n\",\n    \"# loop over the images, turn them into a PIL image\\n\",\n    \"i = 0\\n\",\n    \"for col in range(10):\\n\",\n    \"    for row in range(10):\\n\",\n    \"        array = samples[i]\\n\",\n    \"        array = ((array / max(array)) * 255).reshape((20, 20)).transpose() # redistribute values\\n\",\n    \"        img = Image.fromarray(array)\\n\",\n    \"        display_img.paste(img, (col*20, row*20))\\n\",\n    \"        i += 1\\n\",\n    \"\\n\",\n    \"# present display_img\\n\",\n    \"plt.title('Examples from the dataset')\\n\",\n    \"plt.imshow(display_img, interpolation='nearest')\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 4,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"# Add a bias column to X\\n\",\n    \"bias = np.ones((m,1))\\n\",\n    \"X = np.append(bias, X, axis=1)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Compute the Cost and Gradient\\n\",\n    \"The following functions are copied from [ex2](https://github.com/rickwierenga/CS229-Python/tree/master/ex2).\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 5,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def sigmoid(z):\\n\",\n    \"    return 1 / (1 + np.exp(-z))\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 6,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def compute_regularized_cost(theta, X, y, _lambda):\\n\",\n    \"    m = len(y)\\n\",\n    \"    regularization = _lambda / (2 * m) * np.sum(theta[1:] ** 2) #np.squared()???/\\n\",\n    \"    cost = 1/m * (-y @ np.log(sigmoid(X @ theta)) - (1 - y) @ np.log(1 - sigmoid(X@theta)))\\n\",\n    \"    return cost + regularization\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 7,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def compute_regularized_gradient(theta, X, y, _lambda):\\n\",\n    \"    m = len(y)\\n\",\n    \"    n = len(theta)\\n\",\n    \"    gradient = np.ones(n)\\n\",\n    \"    hx = sigmoid(X @ theta)\\n\",\n    \"    gradient = (1 / m) * X.T @ (hx - y)\\n\",\n    \"    regularization = (_lambda / m) * theta\\n\",\n    \"    regularization[0] = 0\\n\",\n    \"        \\n\",\n    \"    return gradient + regularization\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### One-vs-all classification\\n\",\n    \"One-vs-all classification works by finding a decision boundary between every class (denoted $k$) and every example that is not in the class (0). We will store the found values for theta as rows in our matrix $\\\\Theta$ (capital) where every column is are the values of $\\\\theta$ like we had in binary classification.\\n\",\n    \"\\n\",\n    \"In this part of the exercise, you will implement one-vs-all classification by training multiple regularized logistic regression classifiers, one for each of the K classes in our dataset (numbers 0 through 9). In the handwritten digits dataset, $K = 10$, but your code should work for any value of $K$.\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement one-vs-all logistic regression. Your code should return all the classifier parameters in a matrix $\\\\Theta \\\\in \\\\mathbb{R}^{K\\\\times(N+1)}$, where each row of Θ corresponds to the learned logistic regression parameters for one class. `scipy.optimize.minimize` is already imported as `optimize`.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 8,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def train(X, y, K, _lambda):\\n\",\n    \"    n = X.shape[1]\\n\",\n    \"    theta = np.zeros((K, n))\\n\",\n    \"    \\n\",\n    \"    return theta\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 9,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"K = 10\\n\",\n    \"_lambda = 0.1\\n\",\n    \"theta = train(X, y, K, _lambda)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Evaluation\\n\",\n    \"According to the exercise, we should have a 96,46% accuracy over the entire training set using multi-class classification.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 10,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"'Training set accuracy using multi-class classification: 10.0%'\"\n      ]\n     },\n     \"execution_count\": 10,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"# Make sure to add 1 to the result as `y` is one indexed while the prediction is 0 indexed.\\n\",\n    \"accuracy = np.mean(np.argmax(sigmoid(X @ theta.T), axis = 1) + 1 == y) * 100\\n\",\n    \"'Training set accuracy using multi-class classification: {:2}%'.format(accuracy)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Multi-class Classification with Neural Networks\\n\",\n    \"\\n\",\n    \"---\\n\",\n    \"Neural networks are a more advanced model for doing logistic regression. Neural networks are based on the brain. Neurons in the brain are nodes in the network. $x_1, x_2, ... x_n$ are the _input layers_ of the network and the hypothesis $h_\\\\theta(x)$ is the _output layer_. The output layer exists of $\\\\theta_0, \\\\theta_1, ... \\\\theta_n$.\\n\",\n    \"\\n\",\n    \"Between the input layer and output layer are _hidden layer(s)_. Each connection in the network has a weight we previously called \\\"theta parameters\\\". The hidden layers' values are denoted by $a$. $a^j$ is the activation of layer $j$ in the network and $a_i^{(j)}$ is the activation (value) for neuron $i$ in layer $j$. Although networks in theory can have an infinte number of neurons, it is often impraticial to use too many layers at it slows down learning and training dramatically. You should choose the number of hidden layers depending on the complexity of your dataset.\\n\",\n    \"\\n\",\n    \"Each neuron has an _activation function_. In this case we use the sigmoid function.\\n\",\n    \"\\n\",\n    \"For a network consisting of a single layer with 3 neurons in the input and hidden layer with one neuron in the output layer, the proces would like something like: (note that $a_0$ os not shown - it will always be equal to a vector of 1's) \\n\",\n    \"\\n\",\n    \"$$\\\\begin{bmatrix}x_0\\\\\\\\x_1\\\\\\\\x_2\\\\end{bmatrix} \\\\rightarrow \\\\begin{bmatrix}a_0^{(2)} \\\\\\\\a_1^{(2)} \\\\\\\\a_2^{(2)} \\\\end{bmatrix} \\\\rightarrow h_\\\\theta(x)$$\\n\",\n    \"\\n\",\n    \"With a network wired as shown below and the sigmoid function, $g$, as the activation function, we would optain the values for node $a_i^j$ as follows:\\n\",\n    \"\\n\",\n    \"$$a_i^{(j)} = g(\\\\Theta_{i,0}^{(i-j)}x_0 + \\\\Theta_{i,1}^{(i-j)}x_1 + ... + \\\\Theta_{i,n}^{(i-j)}x_n)$$\\n\",\n    \"\\n\",\n    \"We can vectorize that as:\\n\",\n    \"\\n\",\n    \"$$a_i^{(j)} = g(\\\\theta^{(j-1)}x^{(j-1)})$$\\n\",\n    \"\\n\",\n    \"Our neural network is shown in the image below. Since the images are of size 20×20, this gives us 400 input layer units (excluding the extra bias unit which always outputs +1)\\n\",\n    \"\\n\",\n    \"<div>\\n\",\n    \"    <img style='max-width:40%;' src='notes/model.png'>\\n\",\n    \"</div>\\n\",\n    \"\\n\",\n    \"In this part of the exercise, you will implement a neural network to recognize handwritten digits using the same training set as before. The neural network will be able to represent complex models that form non-linear hypotheses. For this week, you will be using parameters from a neural network that we have already trained. Your goal is to implement the feedforward propagation algorithm to use our weights for prediction. In next week’s exercise, you will write the backpropagation algorithm for learning the neural network parameters.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 11,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"((25, 401), (10, 26))\"\n      ]\n     },\n     \"execution_count\": 11,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"# load the pretrained weights\\n\",\n    \"theta = sio.loadmat(\\\"ex3weights.mat\\\")\\n\",\n    \"theta_1 = theta['Theta1']\\n\",\n    \"theta_2 = theta['Theta2']\\n\",\n    \"theta_1.shape, theta_2.shape\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Feedforward propogation\\n\",\n    \"\\n\",\n    \"Feedforward propogation is the routing of the data throught the neueral network to get a prediction. In multi-class classificiation, the output layer of the network exists of multiple neurons. The output of the network, therefore, is a vector consisisting of probalities for each class. Remember the formula for forwarding data described above.\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement the feedforward computation that computes $h_\\\\theta(x^{(i)})$ for every example i and returns the associated predictions. Similar to the one-vs-all classification strategy, the prediction from the neural network will be the label that has the largest output $(h_\\\\theta(x))_k$.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 15,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def add_bias(X):\\n\",\n    \"    bias = np.ones((m,1))\\n\",\n    \"    X = np.append(bias, X, axis=1)\\n\",\n    \"    return X\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 22,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def forward(theta, X):\\n\",\n    \"    return X\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 23,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"layer2_activation = add_bias(forward(theta_1, X))\\n\",\n    \"predictions = forward(theta_2, layer2_activation)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Evaluation\\n\",\n    \"According to the exercise, we should have a 97,52% accuracy over the entire training set using neural networks.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 24,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"'Training set accuracy using neural networks: 0.96%'\"\n      ]\n     },\n     \"execution_count\": 24,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"# Make sure to add 1 to the result as `y` is one indexed while `predictions` is 0 indexed.\\n\",\n    \"accuracy = np.mean(np.argmax(sigmoid(predictions), axis = 1) + 1 == y) * 100\\n\",\n    \"'Training set accuracy using neural networks: {:2}%'.format(accuracy)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Let's make a couple of predictions using the neural network. Most predictions should be correct.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 25,\n   \"metadata\": {\n    \"scrolled\": true\n   },\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"'The neural network predicts 110 and the correct answer is 7. This means that it got the answer wrong.'\"\n      ]\n     },\n     \"execution_count\": 25,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"i = random.randint(0, m)\\n\",\n    \"prediction = np.argmax(sigmoid(predictions[i])) + 1\\n\",\n    \"answer = y[i]\\n\",\n    \"\\n\",\n    \"'The neural network predicts {} and the correct answer is {}. This means that it got the answer {}.' \\\\\\n\",\n    \".format(prediction, answer, 'right' if prediction == answer else 'wrong')\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": null,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": []\n  }\n ],\n \"metadata\": {\n  \"kernelspec\": {\n   \"display_name\": \"Python 3\",\n   \"language\": \"python\",\n   \"name\": \"python3\"\n  },\n  \"language_info\": {\n   \"codemirror_mode\": {\n    \"name\": \"ipython\",\n    \"version\": 3\n   },\n   \"file_extension\": \".py\",\n   \"mimetype\": \"text/x-python\",\n   \"name\": \"python\",\n   \"nbconvert_exporter\": \"python\",\n   \"pygments_lexer\": \"ipython3\",\n   \"version\": \"3.7.1\"\n  }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n"
  },
  {
    "path": "ex4/PE4 - Learning Neural Networks (Exercises).ipynb",
    "content": "{\n \"cells\": [\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"# Neural Networks Learning\\n\",\n    \"\\n\",\n    \"Stanford CS229 - Machine Learning by Andrew Ng. Programming exercise 4.\\n\",\n    \"\\n\",\n    \"Please check out [the repository on GitHub](https://github.com/rickwierenga/CS229-Python/). If you spot any mistakes or inconcistencies, please create an issue. For questions you can find me on Twitter: [@rickwierenga](https://twitter.com/rickwierenga). Starring the project on GitHub means a ton to me!\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 1,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"import numpy as np\\n\",\n    \"import pandas as pd\\n\",\n    \"import matplotlib.pylab as plt\\n\",\n    \"from scipy.optimize import minimize\\n\",\n    \"%matplotlib inline\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Neural networks\\n\",\n    \"\\n\",\n    \"---\\n\",\n    \"In the previous exercise, you implemented feedforward propagation for neural networks and used it to predict handwritten digits with the weights we provided. In this exercise, you will implement the backpropagation algorithm to learn the parameters for the neural network.\\n\",\n    \"\\n\",\n    \"Load the data and view some samples in the same way as [ex3](https://github.com/rickwierenga/CS229-Python/tree/master/ex3).\\n\",\n    \"\\n\",\n    \"Remember the output of a neural network: $h_\\\\Theta(x) \\\\in \\\\mathbb{R}^K$. We want y to be a 2 dimensional vector in the form that are network should output. For example, we would represent the output 1 as:\\n\",\n    \"\\n\",\n    \"$\\\\begin{bmatrix}0\\\\\\\\1\\\\\\\\0\\\\\\\\0\\\\\\\\0\\\\\\\\0\\\\\\\\0\\\\\\\\0\\\\\\\\0\\\\\\\\0\\\\end{bmatrix}$\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 2,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def remap(y, K):\\n\",\n    \"    m = len(y)\\n\",\n    \"    out = np.zeros((m, K))\\n\",\n    \"    for index in range(m):\\n\",\n    \"        out[index][y[index] - 1] = 1\\n\",\n    \"    return out\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 3,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"import scipy.io as sio\\n\",\n    \"\\n\",\n    \"# Load data\\n\",\n    \"data = sio.loadmat(\\\"ex4data1.mat\\\")\\n\",\n    \"X = data[\\\"X\\\"]\\n\",\n    \"y = data[\\\"y\\\"]\\n\",\n    \"y = y.reshape(len(y))\\n\",\n    \"\\n\",\n    \"# Initialize some useful variables\\n\",\n    \"m, n = X.shape\\n\",\n    \"input_layer_size = 400\\n\",\n    \"hidden_layer_size = 25\\n\",\n    \"K = 10 # number of classes / output_layer_size\\n\",\n    \"\\n\",\n    \"# remap y\\n\",\n    \"mapped_y = remap(y, K)\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 4,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"<matplotlib.image.AxesImage at 0x10449d518>\"\n      ]\n     },\n     \"execution_count\": 4,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"import random\\n\",\n    \"from PIL import Image\\n\",\n    \"\\n\",\n    \"# get 100 random images from the dataset\\n\",\n    \"num_samples = 100\\n\",\n    \"samples = random.sample(list(X), num_samples)\\n\",\n    \"display_img = Image.new('RGB', (200, 200))\\n\",\n    \"\\n\",\n    \"# loop over the images, turn them into a PIL image\\n\",\n    \"i = 0\\n\",\n    \"for col in range(10):\\n\",\n    \"    for row in range(10):\\n\",\n    \"        array = samples[i]\\n\",\n    \"        array = ((array / max(array)) * 255).reshape((20, 20)).transpose() # redistribute values\\n\",\n    \"        img = Image.fromarray(array)\\n\",\n    \"        display_img.paste(img, (col*20, row*20))\\n\",\n    \"        i += 1\\n\",\n    \"\\n\",\n    \"# present display_img\\n\",\n    \"plt.title('Examples from the dataset')\\n\",\n    \"plt.imshow(display_img, interpolation='nearest')\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Load the provided weights.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 5,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"# load the pretrained weights\\n\",\n    \"theta = sio.loadmat(\\\"ex4weights.mat\\\")\\n\",\n    \"theta_1 = theta['Theta1']\\n\",\n    \"theta_2 = theta['Theta2']\\n\",\n    \"nn_params = np.concatenate([theta_1.flatten(), theta_2.flatten()])\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Feedforward\\n\",\n    \"These are the functions for doing feedforward as written [ex3](https://github.com/rickwierenga/CS229-Python/tree/master/ex3).\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 6,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def sigmoid(z):\\n\",\n    \"    return 1 / (1 + np.exp(-z))\\n\",\n    \"\\n\",\n    \"def add_bias(X):\\n\",\n    \"    m = len(X)\\n\",\n    \"    bias = np.ones(m)\\n\",\n    \"    X = np.vstack((bias, X.T)).T\\n\",\n    \"    return X\\n\",\n    \"\\n\",\n    \"def forward(theta, X):\\n\",\n    \"    return sigmoid(theta @ X)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Cost Function\\n\",\n    \"\\n\",\n    \"Remember the following variables from the lectures: \\n\",\n    \"\\n\",\n    \"* $L$: Total number of layers in the network\\n\",\n    \"* $s_l$: number of units (not counting bias unit) in layer $l$.\\n\",\n    \"* $K$: number of output classes\\n\",\n    \"\\n\",\n    \"The cost function for neural networks without regularization:\\n\",\n    \"\\n\",\n    \"$$J(\\\\theta) = \\\\frac{1}{m}\\\\displaystyle\\\\sum_{i=1}^{m}\\\\displaystyle\\\\sum_{k=1}^{K}\\\\begin{bmatrix} -y^{(i)}_k \\\\log (h_\\\\theta(x^{(i)}) - (1 - y^{(i)})_k \\\\log(1-(h_\\\\theta(x^{(i)}))_k)\\\\end{bmatrix}$$\\n\",\n    \"\\n\",\n    \"And with regularization:\\n\",\n    \"\\n\",\n    \"$$J(\\\\theta) = -\\\\frac{1}{m}\\\\displaystyle\\\\sum_{i=1}^{m}\\\\displaystyle\\\\sum_{k=1}^{K}\\\\begin{bmatrix} -y^{(i)}_k \\\\log ((h_\\\\theta(x^{(i)}-(1-y^{(i)})_k) \\\\log(1-(h_\\\\theta(x^{(i)}))_k)\\\\end{bmatrix} + \\\\frac{\\\\lambda}{2m} \\\\displaystyle\\\\sum_{l=1}^{L-1}\\\\displaystyle\\\\sum_{i=1}^{s_l}\\\\displaystyle\\\\sum_{j=1}^{s_l+1}(\\\\Theta^{(l)}_{ji})^2$$\\n\",\n    \"\\n\",\n    \"The double sum adds up the costs for each cell in the output layer. The triple sum adds up the squares of all $\\\\Theta$s in the network.\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement the cost function for neural networks, `compute_nn_cost`, in Python. There are some structural comments to help you.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 7,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def compute_nn_cost(nn_params, X, y, input_layer_size, hidden_layer_size, K, _lambda=0):\\n\",\n    \"    m = len(y)\\n\",\n    \"    \\n\",\n    \"    # Extract theta_1 and theta_2 from nn_params\\n\",\n    \"    \\n\",\n    \"    # Feed forward the network to get the predictions\\n\",\n    \"    \\n\",\n    \"    # Compute the cost of the current prediction\\n\",\n    \"    network_cost = 0\\n\",\n    \"    regularization = 0\\n\",\n    \"\\n\",\n    \"    return network_cost + regularization\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 8,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"Cost without regularization:  0% (0.29 approx)\\n\",\n      \"Cost with regularization:  0% (0.38 approx)\\n\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"J = compute_nn_cost(nn_params, X, mapped_y,\\n\",\n    \"                    input_layer_size=input_layer_size,\\n\",\n    \"                    hidden_layer_size=hidden_layer_size,\\n\",\n    \"                    K=10)\\n\",\n    \"_lambda = 1\\n\",\n    \"J_reg = compute_nn_cost(nn_params, X, mapped_y,\\n\",\n    \"                        input_layer_size=input_layer_size,\\n\",\n    \"                        hidden_layer_size=hidden_layer_size,\\n\",\n    \"                        K=10,\\n\",\n    \"                        _lambda=_lambda)\\n\",\n    \"\\n\",\n    \"print('Cost without regularization: {:2}% (0.29 approx)'.format(J))\\n\",\n    \"print('Cost with regularization: {:2}% (0.38 approx)'.format(J_reg))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Backpropogation\\n\",\n    \"\\n\",\n    \"---\\n\",\n    \"\\n\",\n    \"### The Algorithm\\n\",\n    \"As the name suggests, backpropogation is roughly the opposite of feedforward propogation. Backpropogation is an algorithm that trains neural networks by computing the gradient and thereupon applying it to the neural network.\\n\",\n    \"\\n\",\n    \"Backpropogation (Backprop) starts at the end of the network. It finds the difference between the output of the neural network and the desired output. This value gets stored in $\\\\delta_j^{(l)}$, the error/cost for $a_j^{(l)}$. Also, $\\\\frac{\\\\delta}{\\\\delta z_j^{(l)}} = \\\\delta_j^{(l)}$. The process formaly:\\n\",\n    \"\\n\",\n    \"$$\\\\delta_j^{(l)} = a_j^{(l)} - y_j$$ for $l = L$\\n\",\n    \"\\n\",\n    \"$$\\\\delta_j^{(l)} = (\\\\Theta^{(l)})^T\\\\delta^{(l+1)} .* g'(z^{(l)}) = (\\\\Theta^{(l)})^T\\\\delta^{(l+1)} .* \\\\delta^{(l)}$$ for $L > l > 1$\\n\",\n    \"\\n\",\n    \"Also: \\n\",\n    \"\\n\",\n    \"$$D^{(l)}_{ij} = \\\\frac{\\\\delta}{\\\\delta \\\\Theta_j^{(l)}}J(\\\\Theta)$$\\n\",\n    \"\\n\",\n    \"As you would probably have expected, we don't apply the gradient to the input layer, layer 1, because we don't want to change our input in order to get a better output.\\n\",\n    \"\\n\",\n    \"The complete algorithm:\\n\",\n    \"\\n\",\n    \"Set $\\\\Delta^{(l)}_{ij} = 0$ for all ($l$, $i$, $j$)\\n\",\n    \"\\n\",\n    \"for $i = $ to $m$\\n\",\n    \"1. Perform forward propogation to compute $a^{(l)}$ for $l = 2, 3, ..., L$\\n\",\n    \"2. Using $y^{(l)}$, compute $\\\\delta^{(L)} = a^{(L)} - y^{(i)}$\\n\",\n    \"3. Compute $\\\\delta^{(L-2)}$, ..., $\\\\delta^{(2)}$\\n\",\n    \"4. $\\\\Delta^{(l)}_{ij} := \\\\Delta^{(l)}_{ij} + a^{(l)}_j\\\\delta^{(l+1)}_i$\\n\",\n    \"\\n\",\n    \"$D^{(l)}_{i0} = \\\\frac{1}{m}\\\\Delta^{(l)}_{i0}$\\n\",\n    \"\\n\",\n    \"$D^{(l)}_{ij} = \\\\frac{1}{m}\\\\Delta^{(l)}_{ij} + \\\\lambda\\\\Theta^{(l)}_{ij}$ if y $\\\\neq 0$\\n\",\n    \"\\n\",\n    \"### Gradient Checking\\n\",\n    \"After you've implemented code to compute the gradient, it's often a good idea to validate your code by comparing the gradient to an approximation of it. The approximiation is defined as: \\n\",\n    \"\\n\",\n    \"$$\\\\frac{J(\\\\theta+\\\\epsilon) - J(\\\\theta-\\\\epsilon)}{2\\\\epsilon} \\\\approx D$$\\n\",\n    \"\\n\",\n    \"### Random Initialization\\n\",\n    \"\\n\",\n    \"If all values in the neural networks are the same, the neural network will fail to develop advanced patterns and it will not function. This is the reason we use a random value for theta as the initial input (break the symmetry).\\n\",\n    \"\\n\",\n    \"### Neural Network Traning\\n\",\n    \"Follow these steps when training a neural network:\\n\",\n    \"1. Randomly initialize weights (avoid **symmetric ... **)\\n\",\n    \"2. Implement forward propogation to get $h_\\\\Theta(x^{(i)})$ from any $x^{(i)}$.\\n\",\n    \"3. Implement code to compute cost function $J(\\\\Theta)$.\\n\",\n    \"4. Implement backprop to compute partial derrivatives $\\\\frac{\\\\delta}{\\\\delta \\\\Theta^{(l)}_{jk}}J(\\\\Theta)$. \\n\",\n    \"    * Usually with a for loop over the training examples:\\n\",\n    \"        * Perform forward and backward propogation using one example\\n\",\n    \"        * Get activations $a^{(l)}$ and delta terms $d^{(l)}$ for $l = 2, ..., L$\\n\",\n    \"5. Use gradient checking to compare $\\\\frac{\\\\delta}{\\\\delta \\\\Theta^{(l)}_{jk}}J(\\\\Theta)$ computed using back propogation vs. using numerical estate of gradient of $J(\\\\Theta)$. Then disable gradient checking code.\\n\",\n    \"6. Use gradient descent or advanced optimization method with backpropogation to try to minimize $J(\\\\Theta)$ as a function of parameters $\\\\Theta$.\\n\",\n    \"\\n\",\n    \"---\\n\",\n    \"\\n\",\n    \"In this part of the exercise, you will implement the backpropagation algorithm to compute the gradient for the neural network cost function. Once you have computed the gradient, you will be able to train the neural network by minimizing the cost function $J(\\\\theta)$ using an advanced optimization algorithm such as cg.\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Sigmoid Gradient\\n\",\n    \"**Exercise**: Implement the gradient for the sigmoid function.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 9,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def sigmoid_gradient(z):\\n\",\n    \"    return z\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Initializing Parameters\\n\",\n    \"**Exercise**: Initialize random weights.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 10,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def initialize_random_weights(L_in, L_out):\\n\",\n    \"    epsilon = 0.12\\n\",\n    \"    W = np.zeros((L_out, L_in + 1))\\n\",\n    \"    return W\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 11,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"initial_theta_1 = initialize_random_weights(input_layer_size, hidden_layer_size)\\n\",\n    \"initial_theta_2 = initialize_random_weights(hidden_layer_size, K)\\n\",\n    \"initial_nn_parameters = np.concatenate([initial_theta_1.flatten(), initial_theta_2.flatten()])\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Implement backpropogation\\n\",\n    \"**Exercise**: Implement back propogation in Python\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 12,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def backprop_gradient(nn_params, X, y, input_layer_size, hidden_layer_size, K, _lambda=None):\\n\",\n    \"    return nn_params\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 13,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"# This cell contains functions for testing the gradient. You do not have to understand them.\\n\",\n    \"def debug_initialize_weights(fan_out, fan_in):\\n\",\n    \"    W = np.sin(np.arange(1, (fan_in + 1) * fan_out + 1)) / 10\\n\",\n    \"    return W.reshape(fan_out, fan_in + 1)\\n\",\n    \"\\n\",\n    \"def compute_numerical_gradient(cost_function, nn_params, X, y, input_layer_size, hidden_layer_size, K, _lambda):\\n\",\n    \"    numgrad = np.zeros(nn_params.shape)\\n\",\n    \"    perturb = np.zeros(nn_params.shape)\\n\",\n    \"    e = 1e-4\\n\",\n    \"    for p in range(len(nn_params)):\\n\",\n    \"        # Set pertubation vector\\n\",\n    \"        perturb[p] = e\\n\",\n    \"        loss_1 = cost_function(nn_params-perturb, X, y, \\n\",\n    \"                               input_layer_size=input_layer_size, \\n\",\n    \"                               hidden_layer_size=hidden_layer_size, \\n\",\n    \"                               K=K, \\n\",\n    \"                               _lambda=_lambda)\\n\",\n    \"        loss_2 = cost_function(nn_params+perturb, X, y, \\n\",\n    \"                               input_layer_size=input_layer_size, \\n\",\n    \"                               hidden_layer_size=hidden_layer_size, \\n\",\n    \"                               K=K, \\n\",\n    \"                               _lambda=_lambda)\\n\",\n    \"        \\n\",\n    \"        # Compute numerical gradient\\n\",\n    \"        numgrad[p] = (loss_2 - loss_1) / (2*e)\\n\",\n    \"        perturb[p] = 0\\n\",\n    \"    return numgrad\\n\",\n    \"\\n\",\n    \"def check_gradient(cost_function, gradient_function, _lambda=0):\\n\",\n    \"    \\\"\\\"\\\" Check the gradient function \\\"\\\"\\\"\\n\",\n    \"\\n\",\n    \"    # Initialize test values\\n\",\n    \"    input_layer_size = 3\\n\",\n    \"    hidden_layer_size = 5\\n\",\n    \"    K = 3\\n\",\n    \"    m = 5\\n\",\n    \"    \\n\",\n    \"    theta_1 = debug_initialize_weights(hidden_layer_size, input_layer_size)\\n\",\n    \"    theta_2 = debug_initialize_weights(K, hidden_layer_size)\\n\",\n    \"    X = debug_initialize_weights(m, input_layer_size - 1)\\n\",\n    \"    y = 1 + np.mod(np.arange(1, m+1), K)\\n\",\n    \"    out = np.zeros((m, K))\\n\",\n    \"    for index in range(m):\\n\",\n    \"        out[index][y[index] - 1] = 1\\n\",\n    \"    y = out\\n\",\n    \"    \\n\",\n    \"    # Unroll parameters\\n\",\n    \"    nn_params = np.concatenate([theta_1.flatten(), theta_2.flatten()])\\n\",\n    \"    \\n\",\n    \"    # Compute gradient via backprop\\n\",\n    \"    backprop_gradient = gradient_function(nn_params, X, y,\\n\",\n    \"                                          input_layer_size=input_layer_size,\\n\",\n    \"                                          hidden_layer_size=hidden_layer_size,\\n\",\n    \"                                          K=K,\\n\",\n    \"                                          _lambda=_lambda)\\n\",\n    \"    \\n\",\n    \"    # Compute numerical gradient\\n\",\n    \"    numerical_gradient = compute_numerical_gradient(cost_function, nn_params, X, y,\\n\",\n    \"                                                    input_layer_size=input_layer_size,\\n\",\n    \"                                                    hidden_layer_size=hidden_layer_size,\\n\",\n    \"                                                    K=K,\\n\",\n    \"                                                    _lambda=_lambda)\\n\",\n    \"    \\n\",\n    \"    # Compare the backprop and numerical gradient\\n\",\n    \"    gradients = pd.DataFrame({'Backprop': backprop_gradient, \\n\",\n    \"                              'Numerical': numerical_gradient, \\n\",\n    \"                              'Difference':np.abs(backprop_gradient - numerical_gradient)})\\n\",\n    \"    pd.options.display.max_rows = 5\\n\",\n    \"    print(gradients)\\n\",\n    \"    \\n\",\n    \"    # Compute the difference\\n\",\n    \"    diff = np.linalg.norm(numerical_gradient - backprop_gradient) / np.linalg.norm(backprop_gradient + numerical_gradient)\\n\",\n    \"    print('If the backprop gradient is computed well, the relative diffrence will be no more than 1e-9: {}'.format(diff))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Test the backpropogation algorithm (with and without regularization)\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 14,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"The gradients without regularization: \\n\",\n      \"    Backprop  Numerical  Difference\\n\",\n      \"0   0.084147        0.0    0.084147\\n\",\n      \"1   0.090930        0.0    0.090930\\n\",\n      \"..       ...        ...         ...\\n\",\n      \"36 -0.096140        0.0    0.096140\\n\",\n      \"37 -0.075099        0.0    0.075099\\n\",\n      \"\\n\",\n      \"[38 rows x 3 columns]\\n\",\n      \"If the backprop gradient is computed well, the relative diffrence will be no more than 1e-9: 1.0\\n\",\n      \"\\n\",\n      \"-------------\\n\",\n      \"\\n\",\n      \"The gradients with regularization (lambda=3): \\n\",\n      \"    Backprop  Numerical  Difference\\n\",\n      \"0   0.084147        0.0    0.084147\\n\",\n      \"1   0.090930        0.0    0.090930\\n\",\n      \"..       ...        ...         ...\\n\",\n      \"36 -0.096140        0.0    0.096140\\n\",\n      \"37 -0.075099        0.0    0.075099\\n\",\n      \"\\n\",\n      \"[38 rows x 3 columns]\\n\",\n      \"If the backprop gradient is computed well, the relative diffrence will be no more than 1e-9: 1.0\\n\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"print('The gradients without regularization: ')\\n\",\n    \"check_gradient(compute_nn_cost, backprop_gradient)\\n\",\n    \"\\n\",\n    \"print('\\\\n-------------\\\\n')\\n\",\n    \"\\n\",\n    \"print('The gradients with regularization (lambda=3): ')\\n\",\n    \"check_gradient(compute_nn_cost, backprop_gradient, _lambda=3)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Training the neural network\\n\",\n    \"\\n\",\n    \"The neural network will now be trained using your functions.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 15,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"Optimization terminated successfully.\\n\",\n      \"         Current function value: 0.000000\\n\",\n      \"         Iterations: 0\\n\",\n      \"         Function evaluations: 1\\n\",\n      \"         Gradient evaluations: 1\\n\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"# Get random initial values for theta\\n\",\n    \"initial_theta_1 = initialize_random_weights(input_layer_size, hidden_layer_size)\\n\",\n    \"initial_theta_2 = initialize_random_weights(hidden_layer_size, K)\\n\",\n    \"initial_nn_parameters = np.concatenate([initial_theta_1.flatten(), initial_theta_2.flatten()])\\n\",\n    \"\\n\",\n    \"# Set config\\n\",\n    \"_lambda = 1\\n\",\n    \"args = (X, mapped_y, input_layer_size, hidden_layer_size, K, _lambda)\\n\",\n    \"\\n\",\n    \"# Train NN\\n\",\n    \"result = minimize(compute_nn_cost, initial_nn_parameters, args=args,\\n\",\n    \"                            method='CG', jac=backprop_gradient, \\n\",\n    \"                            options={\\\"maxiter\\\": 50, \\\"disp\\\" : 1})\\n\",\n    \"nn_params = result.x\\n\",\n    \"theta_1 = nn_params[:hidden_layer_size * (input_layer_size + 1)].reshape((hidden_layer_size, (input_layer_size + 1)))\\n\",\n    \"theta_2 = nn_params[(hidden_layer_size * (input_layer_size + 1)):].reshape((K, (hidden_layer_size + 1)))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Visualising the hidden layer\\n\",\n    \"\\n\",\n    \"You can now \\\"visualize\\\" what the neural network is learning by displaying the hidden units to see what features they are capturing in the data.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 16,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stderr\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/ipykernel_launcher.py:11: RuntimeWarning: invalid value encountered in true_divide\\n\",\n      \"  # This is added back by InteractiveShellApp.init_path()\\n\"\n     ]\n    },\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"<matplotlib.image.AxesImage at 0x11e082ef0>\"\n      ]\n     },\n     \"execution_count\": 16,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"# get 100 random images from the dataset\\n\",\n    \"num_samples = 100\\n\",\n    \"hidden_unit_visual = theta_1[:, 1:]\\n\",\n    \"display_img = Image.new('RGB', (100, 100))\\n\",\n    \"\\n\",\n    \"# loop over the images, turn them into a PIL image\\n\",\n    \"i = 0\\n\",\n    \"for col in range(5):\\n\",\n    \"    for row in range(5):\\n\",\n    \"        array = hidden_unit_visual[i]\\n\",\n    \"        array = ((array / max(array)) * 255).reshape((20, 20)).transpose() # redistribute values\\n\",\n    \"        img = Image.fromarray(array)\\n\",\n    \"        display_img.paste(img, (col*20, row*20))\\n\",\n    \"        i += 1\\n\",\n    \"\\n\",\n    \"# present display_img\\n\",\n    \"plt.title('Visualisation of hidden layer 1')\\n\",\n    \"plt.imshow(display_img, interpolation='nearest')\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Evaluating the model\\n\",\n    \"\\n\",\n    \"Get the accuracy on the training set for the trained values of theta. According to the exercise, you should have an accuracy of about 95%. However, this may vary due to the random initalization.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 17,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"'Training set accuracy using the a neural network with the trained values for theta: 10.0%'\"\n      ]\n     },\n     \"execution_count\": 17,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"# Make sure to add 1 to the result as `y` is one indexed while the prediction is 0 indexed.\\n\",\n    \"layer2_activation = add_bias(forward(theta_1, add_bias(X).T).T).T\\n\",\n    \"predictions = forward(theta_2, layer2_activation).T\\n\",\n    \"\\n\",\n    \"accuracy = np.mean(np.argmax(predictions, axis = 1) + 1 == y) * 100\\n\",\n    \"'Training set accuracy using the a neural network with the trained values for theta: {:2}%'.format(accuracy)\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": null,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": []\n  }\n ],\n \"metadata\": {\n  \"kernelspec\": {\n   \"display_name\": \"Python 3\",\n   \"language\": \"python\",\n   \"name\": \"python3\"\n  },\n  \"language_info\": {\n   \"codemirror_mode\": {\n    \"name\": \"ipython\",\n    \"version\": 3\n   },\n   \"file_extension\": \".py\",\n   \"mimetype\": \"text/x-python\",\n   \"name\": \"python\",\n   \"nbconvert_exporter\": \"python\",\n   \"pygments_lexer\": \"ipython3\",\n   \"version\": \"3.7.1\"\n  }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n"
  },
  {
    "path": "ex5/PE5 - Logistic Regression (Exercises).ipynb",
    "content": "{\n \"cells\": [\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"# Regularized Linear Regression and Bias v.s. Variance\\n\",\n    \"\\n\",\n    \"Stanford CS229 - Machine Learning by Andrew Ng. Programming exercise 5.\\n\",\n    \"\\n\",\n    \"Please check out [the repository on GitHub](https://github.com/rickwierenga/CS229-Python/). If you spot any mistakes or inconcistencies, please create an issue. For questions you can find me on Twitter: [@rickwierenga](https://twitter.com/rickwierenga). Starring the project on GitHub means a ton to me!\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 1,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"import numpy as np\\n\",\n    \"import pandas as pd\\n\",\n    \"import matplotlib.pylab as plt\\n\",\n    \"from scipy.optimize import minimize\\n\",\n    \"%matplotlib inline\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Regularized Linear Regression\\n\",\n    \"\\n\",\n    \"---\\n\",\n    \"In the first half of the exercise, you will implement regularized linear regres- sion to predict the amount of water flowing out of a dam using the change of water level in a reservoir. In the next half, you will go through some diag- nostics of debugging learning algorithms and examine the effects of bias v.s. variance.\\n\",\n    \"\\n\",\n    \"Start by loading the data.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 2,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"import scipy.io as sio\\n\",\n    \"\\n\",\n    \"# Load data\\n\",\n    \"data = sio.loadmat(\\\"ex5data1.mat\\\")\\n\",\n    \"X = data[\\\"X\\\"]\\n\",\n    \"m, n = X.shape\\n\",\n    \"y = data[\\\"y\\\"].reshape(m)\\n\",\n    \"Xval = data['Xval']\\n\",\n    \"mval, nval = Xval.shape\\n\",\n    \"yval = data['yval'].reshape(mval)\\n\",\n    \"\\n\",\n    \"# Add bias to X\\n\",\n    \"X = np.hstack((np.ones((m, 1)), X))\\n\",\n    \"Xval = np.hstack((np.ones((mval, 1)), Xval))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Visualising the data\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 3,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"Text(0, 0.5, 'Water flowing out of the dam (y)')\"\n      ]\n     },\n     \"execution_count\": 3,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"plt.plot(X[:, 1], y, 'rx')\\n\",\n    \"plt.xlabel('Change in water leven (x)')\\n\",\n    \"plt.ylabel('Water flowing out of the dam (y)')\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Recall the cost function for regularized linear regression: \\n\",\n    \"\\n\",\n    \"$$J(\\\\theta) = \\\\frac{1}{m}(\\\\displaystyle\\\\sum_{i=1}^{m}(h_\\\\theta(x^{(i)}) - y^{(i)})^2) + \\\\frac{\\\\lambda}{m}\\\\displaystyle\\\\sum_{j=1}^{n}{\\\\theta_j}^2$$\\n\",\n    \"\\n\",\n    \"**Exercise**: Write a regularized vectorized linear regression function.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 4,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def linear_reg_cost_function(theta, X, y, _lambda):\\n\",\n    \"    m = len(y)\\n\",\n    \"    cost = 0\\n\",\n    \"    regularization = 0\\n\",\n    \"    return cost + regularization\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"According to the exercise, using ones for theta should return 303.993 as intial cost.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 5,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"0\"\n      ]\n     },\n     \"execution_count\": 5,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"initial_theta = np.ones(2)\\n\",\n    \"linear_reg_cost_function(initial_theta, X, y, _lambda=1)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Regularized linear regression gradient\\n\",\n    \"\\n\",\n    \"The partial derrivatives for $\\\\theta_j$:\\n\",\n    \"\\n\",\n    \"$$\\\\frac{\\\\delta J(\\\\theta)}{\\\\delta\\\\theta_j} = \\\\frac{1}{m}\\\\displaystyle\\\\sum_{i=1}^{m}(h_\\\\theta(x^{(i)}) - y^{(i)})x_i^{(i)}$$ for $j=0$\\n\",\n    \"\\n\",\n    \"$$\\\\frac{\\\\delta J(\\\\theta)}{\\\\delta\\\\theta_j} = (\\\\frac{1}{m}\\\\displaystyle\\\\sum_{i=1}^{m}(h_\\\\theta(x^{(i)}) - y^{(i)})x_i^{(i)}) + \\\\frac{\\\\lambda}{m}\\\\theta_j$$ for $j\\\\geqslant 1$\\n\",\n    \"\\n\",\n    \"Vectorized: \\n\",\n    \"\\n\",\n    \"$$\\\\frac{\\\\delta J(\\\\theta)}{\\\\delta\\\\theta_j} = \\\\frac{1}{m} \\\\cdot X^T \\\\cdot (X\\\\theta - \\\\vec{y}) $$\\n\",\n    \"\\n\",\n    \"**Exercise**: Find the partial derrivatives of $J(\\\\theta)$. Your code should not contain any loops.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 6,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def compute_gradient(theta, X, y, _lambda):\\n\",\n    \"    hx = X @ theta\\n\",\n    \"    cost = (1/m) * X.T @ (hx - y)\\n\",\n    \"    regularization = (_lambda/m) * np.concatenate(([0], theta[1:]))\\n\",\n    \"    return cost + regularization\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"You should get the following values: $\\\\begin{bmatrix}-15.30 && 598.250 \\\\end{bmatrix}$.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 7,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"array([-15.30301567, 598.25074417])\"\n      ]\n     },\n     \"execution_count\": 7,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"compute_gradient(initial_theta, X, y, _lambda=1)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Training the mdoel\\n\",\n    \"Now we can train the model using `scipy.optimize.minimize`. In this implementation, we set $\\\\lambda$ to 0.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 8,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"Warning: Desired error not necessarily achieved due to precision loss.\\n\",\n      \"         Current function value: 0.000000\\n\",\n      \"         Iterations: 0\\n\",\n      \"         Function evaluations: 113\\n\",\n      \"         Gradient evaluations: 101\\n\"\n     ]\n    },\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"array([1., 1.])\"\n      ]\n     },\n     \"execution_count\": 8,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"_lambda = 0\\n\",\n    \"args = (X, y, _lambda)\\n\",\n    \"result = minimize(linear_reg_cost_function, initial_theta, args=args,\\n\",\n    \"                  method='CG', jac=compute_gradient,\\n\",\n    \"                  options={'maxiter': 50, 'disp': True})\\n\",\n    \"theta = result.x\\n\",\n    \"theta\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Visualize the found $\\\\theta$\\n\",\n    \"\\n\",\n    \"Althought the found value is not a good value, it's the best conjugate gradient could find using our model.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 9,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"plt.plot(X[:,1], y, 'rx', label='Training data')\\n\",\n    \"plt.plot(X[:,1], X.dot(theta), label='Regression')\\n\",\n    \"plt.legend()\\n\",\n    \"plt.xlabel('Change in water leven (x)')\\n\",\n    \"plt.ylabel('Water flowing out of the dam (y)')\\n\",\n    \"plt.show()\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Bias Variance\\n\",\n    \"Models with high bias are not complex enough for the data and tend to underfit, while models with high variance overfit to the training data.\\n\",\n    \"\\n\",\n    \"### Learning Curves\\n\",\n    \"You will now implement code to generate the learning curves that will be useful in debugging learning algorithms. Recall that a learning curve plots training and cross validation error as a function of training set size.\\n\",\n    \"\\n\",\n    \"This model has a high bias problem.\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement the learning curve function.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 10,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def learning_curve(X, y, Xval, yval, _lambda):\\n\",\n    \"    \\\"\\\"\\\" Get the learning curves for each value of m\\n\",\n    \"    \\n\",\n    \"    Returns:\\n\",\n    \"    :error_train: The training error of the dataset until i\\n\",\n    \"    :error_val:   The error of the _entire_ cross validation set\\n\",\n    \"    \\\"\\\"\\\"\\n\",\n    \"    m, n = X.shape\\n\",\n    \"    error_train = np.zeros((m, 1))\\n\",\n    \"    error_val   = np.zeros((m, 1))\\n\",\n    \"    \\n\",\n    \"    for i in range(1, m+1):\\n\",\n    \"        pass # remove this line\\n\",\n    \"    \\n\",\n    \"    return error_train, error_val\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 11,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"<matplotlib.legend.Legend at 0x129dc4710>\"\n      ]\n     },\n     \"execution_count\": 11,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"error_train, error_val = learning_curve(X, y, Xval, yval, _lambda)\\n\",\n    \"plt.plot(error_train, label='train')\\n\",\n    \"plt.plot(error_val, label='validation')\\n\",\n    \"plt.legend()\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Polynomial Regression\\n\",\n    \"The problem with our linear model was that it was too simple for the data and resulted in underfitting (high bias). In this part of the exercise, you will address this problem by adding more features.\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement the function that maps the original training set X of size $m \\\\times 1$ into its higher powers. Specifically, when a training set X of size m × 1 is passed into the function, the function should return a $m \\\\times p$ matrix.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 12,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def polynomial_features(X, p):\\n\",\n    \"    return X\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Remember feature scaling:\\n\",\n    \"\\n\",\n    \"$$X := \\\\frac{X - \\\\mu}{\\\\sigma}$$\\n\",\n    \"\\n\",\n    \"Where $\\\\mu$ is the average value of $X$ and $\\\\sigma$ is the standard deviation.\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement feature scaling.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 17,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def scale_features(X):\\n\",\n    \"    return X, 1, 1\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Add polynomial features to $X$ and normalize it.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 18,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"p = 8\\n\",\n    \"\\n\",\n    \"# X\\n\",\n    \"X_poly = polynomial_features(X[:, 1:], p) # ignore the bias column when adding polynomial features.\\n\",\n    \"X_poly, mu, sigma = scale_features(X_poly)\\n\",\n    \"X_poly = np.hstack((np.ones((m, 1)), X_poly))\\n\",\n    \"\\n\",\n    \"# X_val\\n\",\n    \"X_val_poly = polynomial_features(X[:, 1:], p) # ignore the bias column when adding polynomial features.\\n\",\n    \"X_val_poly = (X_val_poly - mu) / sigma\\n\",\n    \"X_val_poly = np.hstack((np.ones((m, 1)), X_val_poly))\\n\",\n    \"\\n\",\n    \"# X_test\\n\",\n    \"X_test_poly = polynomial_features(X[:, 1:], p) # ignore the bias column when adding polynomial features.\\n\",\n    \"X_test_poly = (X_test_poly - mu) / sigma\\n\",\n    \"X_test_poly = np.hstack((np.ones((m, 1)), X_test_poly))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Learning polynomial regression\\n\",\n    \"\\n\",\n    \"This example shows the learning curve and fit without regularization (high variance).\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 19,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"ename\": \"ValueError\",\n     \"evalue\": \"shapes (12,2) and (9,) not aligned: 2 (dim 1) != 9 (dim 0)\",\n     \"output_type\": \"error\",\n     \"traceback\": [\n      \"\\u001b[0;31m---------------------------------------------------------------------------\\u001b[0m\",\n      \"\\u001b[0;31mValueError\\u001b[0m                                Traceback (most recent call last)\",\n      \"\\u001b[0;32m<ipython-input-19-993b16c6456e>\\u001b[0m in \\u001b[0;36m<module>\\u001b[0;34m\\u001b[0m\\n\\u001b[1;32m      4\\u001b[0m result = minimize(linear_reg_cost_function, initial_theta, args=args,\\n\\u001b[1;32m      5\\u001b[0m                   \\u001b[0mmethod\\u001b[0m\\u001b[0;34m=\\u001b[0m\\u001b[0;34m'CG'\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mjac\\u001b[0m\\u001b[0;34m=\\u001b[0m\\u001b[0mcompute_gradient\\u001b[0m\\u001b[0;34m,\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m----> 6\\u001b[0;31m                   options={'maxiter': 1000, 'disp': True})\\n\\u001b[0m\\u001b[1;32m      7\\u001b[0m \\u001b[0mtheta\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mresult\\u001b[0m\\u001b[0;34m.\\u001b[0m\\u001b[0mx\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/scipy/optimize/_minimize.py\\u001b[0m in \\u001b[0;36mminimize\\u001b[0;34m(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)\\u001b[0m\\n\\u001b[1;32m    591\\u001b[0m         \\u001b[0;32mreturn\\u001b[0m \\u001b[0m_minimize_powell\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mfun\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mx0\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0margs\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mcallback\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;34m**\\u001b[0m\\u001b[0moptions\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m    592\\u001b[0m     \\u001b[0;32melif\\u001b[0m \\u001b[0mmeth\\u001b[0m \\u001b[0;34m==\\u001b[0m \\u001b[0;34m'cg'\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m--> 593\\u001b[0;31m         \\u001b[0;32mreturn\\u001b[0m \\u001b[0m_minimize_cg\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mfun\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mx0\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0margs\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mjac\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mcallback\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;34m**\\u001b[0m\\u001b[0moptions\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\\u001b[1;32m    594\\u001b[0m     \\u001b[0;32melif\\u001b[0m \\u001b[0mmeth\\u001b[0m \\u001b[0;34m==\\u001b[0m \\u001b[0;34m'bfgs'\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m    595\\u001b[0m         \\u001b[0;32mreturn\\u001b[0m \\u001b[0m_minimize_bfgs\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mfun\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mx0\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0margs\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mjac\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mcallback\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;34m**\\u001b[0m\\u001b[0moptions\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/scipy/optimize/optimize.py\\u001b[0m in \\u001b[0;36m_minimize_cg\\u001b[0;34m(fun, x0, args, jac, callback, gtol, norm, eps, maxiter, disp, return_all, **unknown_options)\\u001b[0m\\n\\u001b[1;32m   1270\\u001b[0m     \\u001b[0;32melse\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m   1271\\u001b[0m         \\u001b[0mgrad_calls\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mmyfprime\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mwrap_function\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mfprime\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0margs\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m-> 1272\\u001b[0;31m     \\u001b[0mgfk\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mmyfprime\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mx0\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\\u001b[1;32m   1273\\u001b[0m     \\u001b[0mk\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0;36m0\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m   1274\\u001b[0m     \\u001b[0mxk\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mx0\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/scipy/optimize/optimize.py\\u001b[0m in \\u001b[0;36mfunction_wrapper\\u001b[0;34m(*wrapper_args)\\u001b[0m\\n\\u001b[1;32m    298\\u001b[0m     \\u001b[0;32mdef\\u001b[0m \\u001b[0mfunction_wrapper\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;34m*\\u001b[0m\\u001b[0mwrapper_args\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m    299\\u001b[0m         \\u001b[0mncalls\\u001b[0m\\u001b[0;34m[\\u001b[0m\\u001b[0;36m0\\u001b[0m\\u001b[0;34m]\\u001b[0m \\u001b[0;34m+=\\u001b[0m \\u001b[0;36m1\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m--> 300\\u001b[0;31m         \\u001b[0;32mreturn\\u001b[0m \\u001b[0mfunction\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;34m*\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mwrapper_args\\u001b[0m \\u001b[0;34m+\\u001b[0m \\u001b[0margs\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\\u001b[1;32m    301\\u001b[0m \\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m    302\\u001b[0m     \\u001b[0;32mreturn\\u001b[0m \\u001b[0mncalls\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mfunction_wrapper\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;32m<ipython-input-6-9ccef08b4840>\\u001b[0m in \\u001b[0;36mcompute_gradient\\u001b[0;34m(theta, X, y, _lambda)\\u001b[0m\\n\\u001b[1;32m      1\\u001b[0m \\u001b[0;32mdef\\u001b[0m \\u001b[0mcompute_gradient\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mtheta\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mX\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0my\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0m_lambda\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m----> 2\\u001b[0;31m     \\u001b[0mhx\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mX\\u001b[0m \\u001b[0;34m@\\u001b[0m \\u001b[0mtheta\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\\u001b[1;32m      3\\u001b[0m     \\u001b[0mcost\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0;34m(\\u001b[0m\\u001b[0;36m1\\u001b[0m\\u001b[0;34m/\\u001b[0m\\u001b[0mm\\u001b[0m\\u001b[0;34m)\\u001b[0m \\u001b[0;34m*\\u001b[0m \\u001b[0mX\\u001b[0m\\u001b[0;34m.\\u001b[0m\\u001b[0mT\\u001b[0m \\u001b[0;34m@\\u001b[0m \\u001b[0;34m(\\u001b[0m\\u001b[0mhx\\u001b[0m \\u001b[0;34m-\\u001b[0m \\u001b[0my\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m      4\\u001b[0m     \\u001b[0mregularization\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0;34m(\\u001b[0m\\u001b[0m_lambda\\u001b[0m\\u001b[0;34m/\\u001b[0m\\u001b[0mm\\u001b[0m\\u001b[0;34m)\\u001b[0m \\u001b[0;34m*\\u001b[0m \\u001b[0mnp\\u001b[0m\\u001b[0;34m.\\u001b[0m\\u001b[0mconcatenate\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;34m[\\u001b[0m\\u001b[0;36m0\\u001b[0m\\u001b[0;34m]\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mtheta\\u001b[0m\\u001b[0;34m[\\u001b[0m\\u001b[0;36m1\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m]\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m      5\\u001b[0m     \\u001b[0;32mreturn\\u001b[0m \\u001b[0mcost\\u001b[0m \\u001b[0;34m+\\u001b[0m \\u001b[0mregularization\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;31mValueError\\u001b[0m: shapes (12,2) and (9,) not aligned: 2 (dim 1) != 9 (dim 0)\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"_lambda = 0\\n\",\n    \"args = (X_poly, y, _lambda)\\n\",\n    \"initial_theta = np.ones(p+1)\\n\",\n    \"result = minimize(linear_reg_cost_function, initial_theta, args=args,\\n\",\n    \"                  method='CG', jac=compute_gradient,\\n\",\n    \"                  options={'maxiter': 1000, 'disp': True})\\n\",\n    \"theta = result.x\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 20,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"# Plot training data\\n\",\n    \"plt.plot(X[:,1], y, 'rx', label='Training data')\\n\",\n    \"\\n\",\n    \"# Plot polynomial fit\\n\",\n    \"space = np.array(np.arange(np.min(X) - 5, np.max(X) + 5, 0.05)).reshape((1912, 1))\\n\",\n    \"X_poly_plt = polynomial_features(space, p)\\n\",\n    \"X_poly_plt = (X_poly_plt - mu) / sigma\\n\",\n    \"X_poly_plt = np.hstack((np.ones((X_poly_plt.shape[0], 1)), X_poly_plt))\\n\",\n    \"plt.plot(space, X_poly_plt @ theta, '--', label='Polynomial fit')\\n\",\n    \"\\n\",\n    \"# Plot\\n\",\n    \"plt.legend()\\n\",\n    \"plt.xlabel('Change in water leven (x)')\\n\",\n    \"plt.ylabel('Water flowing out of the dam (y)')\\n\",\n    \"plt.show()\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 21,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"<matplotlib.legend.Legend at 0x129f6db00>\"\n      ]\n     },\n     \"execution_count\": 21,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"error_train, error_val = learning_curve(X_poly, y, X_val_poly, y, _lambda)\\n\",\n    \"plt.plot(error_train, label='train')\\n\",\n    \"plt.plot(error_val, label='validation')\\n\",\n    \"plt.title('Learning curve with no regularization')\\n\",\n    \"plt.legend()\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Adjusting the regularization parameter\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 22,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def plot_regularization(_lambda):\\n\",\n    \"    \\\"\\\"\\\" Plot the fit and learning curve for a regularization parameter _lambda \\\"\\\"\\\"\\n\",\n    \"    \\n\",\n    \"    # 1. Fit\\n\",\n    \"    \\n\",\n    \"    # Find theta\\n\",\n    \"    args = (X_poly, y, _lambda)\\n\",\n    \"    initial_theta = np.ones(p+1)\\n\",\n    \"    result = minimize(linear_reg_cost_function, initial_theta, args=args,\\n\",\n    \"                      method='CG', jac=compute_gradient,\\n\",\n    \"                      options={'maxiter': 1000, 'disp': False})\\n\",\n    \"    theta = result.x\\n\",\n    \"    \\n\",\n    \"    # Plot training data\\n\",\n    \"    plt.plot(X[:,1], y, 'rx', label='Training data')\\n\",\n    \"\\n\",\n    \"    # Plot polynomial fit\\n\",\n    \"    space = np.array(np.arange(np.min(X) - 5, np.max(X) + 5, 0.05)).reshape((1912, 1))\\n\",\n    \"    X_poly_plt = polynomial_features(space, p)\\n\",\n    \"    X_poly_plt = (X_poly_plt - mu) / sigma\\n\",\n    \"    X_poly_plt = np.hstack((np.ones((X_poly_plt.shape[0], 1)), X_poly_plt))\\n\",\n    \"    plt.plot(space, X_poly_plt @ theta, '--', label='Polynomial fit')\\n\",\n    \"\\n\",\n    \"    # Plot\\n\",\n    \"    plt.legend()\\n\",\n    \"    plt.xlabel('Change in water leven (x)')\\n\",\n    \"    plt.ylabel('Water flowing out of the dam (y)')\\n\",\n    \"    plt.show()\\n\",\n    \"    \\n\",\n    \"    \\n\",\n    \"    # 2. Learning curve\\n\",\n    \"    \\n\",\n    \"    # Plot learning curve\\n\",\n    \"    error_train, error_val = learning_curve(X_poly, y, X_val_poly, y, _lambda)\\n\",\n    \"    plt.plot(error_train, label='train')\\n\",\n    \"    plt.plot(error_val, label='validation')\\n\",\n    \"    plt.title('Learning curve with no regularization')\\n\",\n    \"    plt.legend()\\n\",\n    \"    \\n\",\n    \"    plt.show()\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 23,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"ename\": \"ValueError\",\n     \"evalue\": \"shapes (12,2) and (9,) not aligned: 2 (dim 1) != 9 (dim 0)\",\n     \"output_type\": \"error\",\n     \"traceback\": [\n      \"\\u001b[0;31m---------------------------------------------------------------------------\\u001b[0m\",\n      \"\\u001b[0;31mValueError\\u001b[0m                                Traceback (most recent call last)\",\n      \"\\u001b[0;32m<ipython-input-23-c915fb53b273>\\u001b[0m in \\u001b[0;36m<module>\\u001b[0;34m\\u001b[0m\\n\\u001b[1;32m      1\\u001b[0m \\u001b[0;31m# Good regularization\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m----> 2\\u001b[0;31m \\u001b[0mplot_regularization\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;36m1\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\",\n      \"\\u001b[0;32m<ipython-input-22-72435cb760ac>\\u001b[0m in \\u001b[0;36mplot_regularization\\u001b[0;34m(_lambda)\\u001b[0m\\n\\u001b[1;32m      9\\u001b[0m     result = minimize(linear_reg_cost_function, initial_theta, args=args,\\n\\u001b[1;32m     10\\u001b[0m                       \\u001b[0mmethod\\u001b[0m\\u001b[0;34m=\\u001b[0m\\u001b[0;34m'CG'\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mjac\\u001b[0m\\u001b[0;34m=\\u001b[0m\\u001b[0mcompute_gradient\\u001b[0m\\u001b[0;34m,\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m---> 11\\u001b[0;31m                       options={'maxiter': 1000, 'disp': False})\\n\\u001b[0m\\u001b[1;32m     12\\u001b[0m     \\u001b[0mtheta\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mresult\\u001b[0m\\u001b[0;34m.\\u001b[0m\\u001b[0mx\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m     13\\u001b[0m \\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/scipy/optimize/_minimize.py\\u001b[0m in \\u001b[0;36mminimize\\u001b[0;34m(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)\\u001b[0m\\n\\u001b[1;32m    591\\u001b[0m         \\u001b[0;32mreturn\\u001b[0m \\u001b[0m_minimize_powell\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mfun\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mx0\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0margs\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mcallback\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;34m**\\u001b[0m\\u001b[0moptions\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m    592\\u001b[0m     \\u001b[0;32melif\\u001b[0m \\u001b[0mmeth\\u001b[0m \\u001b[0;34m==\\u001b[0m \\u001b[0;34m'cg'\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m--> 593\\u001b[0;31m         \\u001b[0;32mreturn\\u001b[0m \\u001b[0m_minimize_cg\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mfun\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mx0\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0margs\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mjac\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mcallback\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;34m**\\u001b[0m\\u001b[0moptions\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\\u001b[1;32m    594\\u001b[0m     \\u001b[0;32melif\\u001b[0m \\u001b[0mmeth\\u001b[0m \\u001b[0;34m==\\u001b[0m \\u001b[0;34m'bfgs'\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m    595\\u001b[0m         \\u001b[0;32mreturn\\u001b[0m \\u001b[0m_minimize_bfgs\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mfun\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mx0\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0margs\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mjac\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mcallback\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;34m**\\u001b[0m\\u001b[0moptions\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/scipy/optimize/optimize.py\\u001b[0m in \\u001b[0;36m_minimize_cg\\u001b[0;34m(fun, x0, args, jac, callback, gtol, norm, eps, maxiter, disp, return_all, **unknown_options)\\u001b[0m\\n\\u001b[1;32m   1270\\u001b[0m     \\u001b[0;32melse\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m   1271\\u001b[0m         \\u001b[0mgrad_calls\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mmyfprime\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mwrap_function\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mfprime\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0margs\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m-> 1272\\u001b[0;31m     \\u001b[0mgfk\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mmyfprime\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mx0\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\\u001b[1;32m   1273\\u001b[0m     \\u001b[0mk\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0;36m0\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m   1274\\u001b[0m     \\u001b[0mxk\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mx0\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/scipy/optimize/optimize.py\\u001b[0m in \\u001b[0;36mfunction_wrapper\\u001b[0;34m(*wrapper_args)\\u001b[0m\\n\\u001b[1;32m    298\\u001b[0m     \\u001b[0;32mdef\\u001b[0m \\u001b[0mfunction_wrapper\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;34m*\\u001b[0m\\u001b[0mwrapper_args\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m    299\\u001b[0m         \\u001b[0mncalls\\u001b[0m\\u001b[0;34m[\\u001b[0m\\u001b[0;36m0\\u001b[0m\\u001b[0;34m]\\u001b[0m \\u001b[0;34m+=\\u001b[0m \\u001b[0;36m1\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m--> 300\\u001b[0;31m         \\u001b[0;32mreturn\\u001b[0m \\u001b[0mfunction\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;34m*\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mwrapper_args\\u001b[0m \\u001b[0;34m+\\u001b[0m \\u001b[0margs\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\\u001b[1;32m    301\\u001b[0m \\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m    302\\u001b[0m     \\u001b[0;32mreturn\\u001b[0m \\u001b[0mncalls\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mfunction_wrapper\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;32m<ipython-input-6-9ccef08b4840>\\u001b[0m in \\u001b[0;36mcompute_gradient\\u001b[0;34m(theta, X, y, _lambda)\\u001b[0m\\n\\u001b[1;32m      1\\u001b[0m \\u001b[0;32mdef\\u001b[0m \\u001b[0mcompute_gradient\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mtheta\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mX\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0my\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0m_lambda\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m----> 2\\u001b[0;31m     \\u001b[0mhx\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mX\\u001b[0m \\u001b[0;34m@\\u001b[0m \\u001b[0mtheta\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\\u001b[1;32m      3\\u001b[0m     \\u001b[0mcost\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0;34m(\\u001b[0m\\u001b[0;36m1\\u001b[0m\\u001b[0;34m/\\u001b[0m\\u001b[0mm\\u001b[0m\\u001b[0;34m)\\u001b[0m \\u001b[0;34m*\\u001b[0m \\u001b[0mX\\u001b[0m\\u001b[0;34m.\\u001b[0m\\u001b[0mT\\u001b[0m \\u001b[0;34m@\\u001b[0m \\u001b[0;34m(\\u001b[0m\\u001b[0mhx\\u001b[0m \\u001b[0;34m-\\u001b[0m \\u001b[0my\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m      4\\u001b[0m     \\u001b[0mregularization\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0;34m(\\u001b[0m\\u001b[0m_lambda\\u001b[0m\\u001b[0;34m/\\u001b[0m\\u001b[0mm\\u001b[0m\\u001b[0;34m)\\u001b[0m \\u001b[0;34m*\\u001b[0m \\u001b[0mnp\\u001b[0m\\u001b[0;34m.\\u001b[0m\\u001b[0mconcatenate\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;34m[\\u001b[0m\\u001b[0;36m0\\u001b[0m\\u001b[0;34m]\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mtheta\\u001b[0m\\u001b[0;34m[\\u001b[0m\\u001b[0;36m1\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m]\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m      5\\u001b[0m     \\u001b[0;32mreturn\\u001b[0m \\u001b[0mcost\\u001b[0m \\u001b[0;34m+\\u001b[0m \\u001b[0mregularization\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;31mValueError\\u001b[0m: shapes (12,2) and (9,) not aligned: 2 (dim 1) != 9 (dim 0)\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"# Good regularization\\n\",\n    \"plot_regularization(1)\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 24,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"ename\": \"ValueError\",\n     \"evalue\": \"shapes (12,2) and (9,) not aligned: 2 (dim 1) != 9 (dim 0)\",\n     \"output_type\": \"error\",\n     \"traceback\": [\n      \"\\u001b[0;31m---------------------------------------------------------------------------\\u001b[0m\",\n      \"\\u001b[0;31mValueError\\u001b[0m                                Traceback (most recent call last)\",\n      \"\\u001b[0;32m<ipython-input-24-7d47b27b02a0>\\u001b[0m in \\u001b[0;36m<module>\\u001b[0;34m\\u001b[0m\\n\\u001b[1;32m      1\\u001b[0m \\u001b[0;31m# (Way) too much regularization\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m----> 2\\u001b[0;31m \\u001b[0mplot_regularization\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;36m100\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\",\n      \"\\u001b[0;32m<ipython-input-22-72435cb760ac>\\u001b[0m in \\u001b[0;36mplot_regularization\\u001b[0;34m(_lambda)\\u001b[0m\\n\\u001b[1;32m      9\\u001b[0m     result = minimize(linear_reg_cost_function, initial_theta, args=args,\\n\\u001b[1;32m     10\\u001b[0m                       \\u001b[0mmethod\\u001b[0m\\u001b[0;34m=\\u001b[0m\\u001b[0;34m'CG'\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mjac\\u001b[0m\\u001b[0;34m=\\u001b[0m\\u001b[0mcompute_gradient\\u001b[0m\\u001b[0;34m,\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m---> 11\\u001b[0;31m                       options={'maxiter': 1000, 'disp': False})\\n\\u001b[0m\\u001b[1;32m     12\\u001b[0m     \\u001b[0mtheta\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mresult\\u001b[0m\\u001b[0;34m.\\u001b[0m\\u001b[0mx\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m     13\\u001b[0m \\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/scipy/optimize/_minimize.py\\u001b[0m in \\u001b[0;36mminimize\\u001b[0;34m(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)\\u001b[0m\\n\\u001b[1;32m    591\\u001b[0m         \\u001b[0;32mreturn\\u001b[0m \\u001b[0m_minimize_powell\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mfun\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mx0\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0margs\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mcallback\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;34m**\\u001b[0m\\u001b[0moptions\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m    592\\u001b[0m     \\u001b[0;32melif\\u001b[0m \\u001b[0mmeth\\u001b[0m \\u001b[0;34m==\\u001b[0m \\u001b[0;34m'cg'\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m--> 593\\u001b[0;31m         \\u001b[0;32mreturn\\u001b[0m \\u001b[0m_minimize_cg\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mfun\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mx0\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0margs\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mjac\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mcallback\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;34m**\\u001b[0m\\u001b[0moptions\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\\u001b[1;32m    594\\u001b[0m     \\u001b[0;32melif\\u001b[0m \\u001b[0mmeth\\u001b[0m \\u001b[0;34m==\\u001b[0m \\u001b[0;34m'bfgs'\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m    595\\u001b[0m         \\u001b[0;32mreturn\\u001b[0m \\u001b[0m_minimize_bfgs\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mfun\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mx0\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0margs\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mjac\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mcallback\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;34m**\\u001b[0m\\u001b[0moptions\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/scipy/optimize/optimize.py\\u001b[0m in \\u001b[0;36m_minimize_cg\\u001b[0;34m(fun, x0, args, jac, callback, gtol, norm, eps, maxiter, disp, return_all, **unknown_options)\\u001b[0m\\n\\u001b[1;32m   1270\\u001b[0m     \\u001b[0;32melse\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m   1271\\u001b[0m         \\u001b[0mgrad_calls\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mmyfprime\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mwrap_function\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mfprime\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0margs\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m-> 1272\\u001b[0;31m     \\u001b[0mgfk\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mmyfprime\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mx0\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\\u001b[1;32m   1273\\u001b[0m     \\u001b[0mk\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0;36m0\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m   1274\\u001b[0m     \\u001b[0mxk\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mx0\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/scipy/optimize/optimize.py\\u001b[0m in \\u001b[0;36mfunction_wrapper\\u001b[0;34m(*wrapper_args)\\u001b[0m\\n\\u001b[1;32m    298\\u001b[0m     \\u001b[0;32mdef\\u001b[0m \\u001b[0mfunction_wrapper\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;34m*\\u001b[0m\\u001b[0mwrapper_args\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m    299\\u001b[0m         \\u001b[0mncalls\\u001b[0m\\u001b[0;34m[\\u001b[0m\\u001b[0;36m0\\u001b[0m\\u001b[0;34m]\\u001b[0m \\u001b[0;34m+=\\u001b[0m \\u001b[0;36m1\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m--> 300\\u001b[0;31m         \\u001b[0;32mreturn\\u001b[0m \\u001b[0mfunction\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;34m*\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mwrapper_args\\u001b[0m \\u001b[0;34m+\\u001b[0m \\u001b[0margs\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\\u001b[1;32m    301\\u001b[0m \\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m    302\\u001b[0m     \\u001b[0;32mreturn\\u001b[0m \\u001b[0mncalls\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mfunction_wrapper\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;32m<ipython-input-6-9ccef08b4840>\\u001b[0m in \\u001b[0;36mcompute_gradient\\u001b[0;34m(theta, X, y, _lambda)\\u001b[0m\\n\\u001b[1;32m      1\\u001b[0m \\u001b[0;32mdef\\u001b[0m \\u001b[0mcompute_gradient\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mtheta\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mX\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0my\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0m_lambda\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m----> 2\\u001b[0;31m     \\u001b[0mhx\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mX\\u001b[0m \\u001b[0;34m@\\u001b[0m \\u001b[0mtheta\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\\u001b[1;32m      3\\u001b[0m     \\u001b[0mcost\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0;34m(\\u001b[0m\\u001b[0;36m1\\u001b[0m\\u001b[0;34m/\\u001b[0m\\u001b[0mm\\u001b[0m\\u001b[0;34m)\\u001b[0m \\u001b[0;34m*\\u001b[0m \\u001b[0mX\\u001b[0m\\u001b[0;34m.\\u001b[0m\\u001b[0mT\\u001b[0m \\u001b[0;34m@\\u001b[0m \\u001b[0;34m(\\u001b[0m\\u001b[0mhx\\u001b[0m \\u001b[0;34m-\\u001b[0m \\u001b[0my\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m      4\\u001b[0m     \\u001b[0mregularization\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0;34m(\\u001b[0m\\u001b[0m_lambda\\u001b[0m\\u001b[0;34m/\\u001b[0m\\u001b[0mm\\u001b[0m\\u001b[0;34m)\\u001b[0m \\u001b[0;34m*\\u001b[0m \\u001b[0mnp\\u001b[0m\\u001b[0;34m.\\u001b[0m\\u001b[0mconcatenate\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;34m[\\u001b[0m\\u001b[0;36m0\\u001b[0m\\u001b[0;34m]\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mtheta\\u001b[0m\\u001b[0;34m[\\u001b[0m\\u001b[0;36m1\\u001b[0m\\u001b[0;34m:\\u001b[0m\\u001b[0;34m]\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m      5\\u001b[0m     \\u001b[0;32mreturn\\u001b[0m \\u001b[0mcost\\u001b[0m \\u001b[0;34m+\\u001b[0m \\u001b[0mregularization\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;31mValueError\\u001b[0m: shapes (12,2) and (9,) not aligned: 2 (dim 1) != 9 (dim 0)\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"# (Way) too much regularization\\n\",\n    \"plot_regularization(100)\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": null,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": []\n  }\n ],\n \"metadata\": {\n  \"kernelspec\": {\n   \"display_name\": \"Python 3\",\n   \"language\": \"python\",\n   \"name\": \"python3\"\n  },\n  \"language_info\": {\n   \"codemirror_mode\": {\n    \"name\": \"ipython\",\n    \"version\": 3\n   },\n   \"file_extension\": \".py\",\n   \"mimetype\": \"text/x-python\",\n   \"name\": \"python\",\n   \"nbconvert_exporter\": \"python\",\n   \"pygments_lexer\": \"ipython3\",\n   \"version\": \"3.7.1\"\n  }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n"
  },
  {
    "path": "ex6/Support Vector Machines (Exercises).ipynb",
    "content": "{\n \"cells\": [\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"# Support Vector Machines\\n\",\n    \"\\n\",\n    \"Stanford CS229 - Machine Learning by Andrew Ng. Programming exercise 6.\\n\",\n    \"\\n\",\n    \"Please check out [the repository on GitHub](https://github.com/rickwierenga/CS229-Python/). If you spot any mistakes or inconcistencies, please create an issue. For questions you can find me on Twitter: [@rickwierenga](https://twitter.com/rickwierenga). Starring the project on GitHub means a ton to me!\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 1,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"import numpy as np\\n\",\n    \"import pandas as pd\\n\",\n    \"import matplotlib.pylab as plt\\n\",\n    \"import scipy.io as sio\\n\",\n    \"%matplotlib inline\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"You should use a support vector machine when \"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Support Vector Machines\\n\",\n    \"---\\n\",\n    \"In the first half of this exercise, you will be using support vector machines (SVMs) with various example 2D datasets. Experimenting with these datasets will help you gain an intuition of how SVMs work and how to use a Gaussian kernel with SVMs. In the next half of the exercise, you will be using support vector machines to build a spam classifier.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 2,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"# Load data\\n\",\n    \"data = sio.loadmat(\\\"ex6data1.mat\\\")\\n\",\n    \"X = data[\\\"X\\\"]\\n\",\n    \"y = data[\\\"y\\\"].flatten()\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Visualising the data\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 3,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"[<matplotlib.lines.Line2D at 0x11e934ef0>]\"\n      ]\n     },\n     \"execution_count\": 3,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"pos = np.where(y==1)[0]\\n\",\n    \"neg = np.where(y==0)[0]\\n\",\n    \"\\n\",\n    \"plt.plot(X[pos, 0], X[pos, 1], 'bx')\\n\",\n    \"plt.plot(X[neg, 0], X[neg, 1], 'yo')\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Training  a linear SVM\\n\",\n    \"Remember: high variance = overfit, high bias = underfit.\\n\",\n    \"\\n\",\n    \"$C$ is the regularization parameter for SVMs where $\\\\lambda$ was the regularization parameter for logistic regression.\\n\",\n    \"\\n\",\n    \"$$C = \\\\frac{1}{\\\\lambda}$$\\n\",\n    \"\\n\",\n    \"Training an SVM in Python can be done using `SciKit Learn`. How this works internally, is beyond the scope of these notebooks.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 4,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"from sklearn.svm import SVC\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 5,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def train_svm(X, y, **params):\\n\",\n    \"    \\\"\\\"\\\" Train an SVM with data X, y and regularization parameter C \\\"\\\"\\\"\\n\",\n    \"    \\n\",\n    \"    model = SVC(**params)\\n\",\n    \"    clf = model.fit(X, y)\\n\",\n    \"    return clf\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 6,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def plot_svm_decision_boundary(clf):\\n\",\n    \"    \\\"\\\"\\\" Plot the decision boundary for an SVM \\\"\\\"\\\"\\n\",\n    \"    w = clf.coef_[0]\\n\",\n    \"    a = -w[0] / w[1]\\n\",\n    \"\\n\",\n    \"    xp = np.array(np.linspace(np.min(X[:, 0]), np.max(X[:, 0]), 100))\\n\",\n    \"    yp = a * xp - (clf.intercept_[0]) / w[1]\\n\",\n    \"    plt.plot(xp, yp, '-k')\\n\",\n    \"    plt.plot(X[pos, 0], X[pos, 1], 'bx')\\n\",\n    \"    plt.plot(X[neg, 0], X[neg, 1], 'yo')\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 7,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"# Decision boundary with C=1. Notice that one example is not classified correctly.\\n\",\n    \"clf = train_svm(X, y, kernel='linear')\\n\",\n    \"plot_svm_decision_boundary(clf)\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 8,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"[1] (51, 2) (51,)\\n\"\n     ]\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"# Decision boundary with C=100. All examples are classified correctly but the boundary does not seem a natural fit.\\n\",\n    \"clf = train_svm(X, y, C=100, kernel='linear')\\n\",\n    \"print(clf.predict(X[0].reshape(1, 2)), X.shape, y.shape)\\n\",\n    \"plot_svm_decision_boundary(clf)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## SVM with Gaussian Kernels\\n\",\n    \"---\\n\",\n    \"To find non-linear decision boundaries with the SVM, we need to first im- plement a Gaussian kernel. You can think of the Gaussian kernel as a sim- ilarity function that measures the “distance” between a pair of examples, $(x^{(i)},x^{(j)})$. The Gaussian kernel is also parameterized by a bandwidth parameter, $\\\\sigma$, which determines how fast the similarity metric decreases (to 0) as the examples are further apart.\\n\",\n    \"\\n\",\n    \"The Gaussian Kernel is defined as:\\n\",\n    \"\\n\",\n    \"$$K_{gaussian}(x^{(i)}, x^{(j)}) = \\\\exp\\\\left(-\\\\frac{\\\\left\\\\lVert x^{(i)} - x^{(j)} \\\\right\\\\rVert ^ 2}{2\\\\sigma^2}\\\\right) = \\\\exp\\\\left(-\\\\frac{\\\\displaystyle\\\\sum_{k=1}^{n}(x_k^{(i)} - x_k^{(j)})^2}{2\\\\sigma^2}\\\\right)$$.\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement the Gaussian kernal function.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 9,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"from sklearn.metrics.pairwise import euclidean_distances\\n\",\n    \"\\n\",\n    \"def gaussian_wrapper(sigma):\\n\",\n    \"    def gaussian_kernel(x1, x2):\\n\",\n    \"        # Placeholder. Remove this line.\\n\",\n    \"        return x1 @ x2.T\\n\",\n    \"    \\n\",\n    \"    return gaussian_kernel\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"The following code should return approximately $0.324652$.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 10,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"array([[7]])\"\n      ]\n     },\n     \"execution_count\": 10,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"x1 = np.array([[1, 2, 1]])\\n\",\n    \"x2 = np.array([[0, 4, -1]])\\n\",\n    \"gaussian_wrapper(2)(x1, x2)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Dataset 2\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 11,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"data = sio.loadmat(\\\"ex6data2.mat\\\")\\n\",\n    \"X = data[\\\"X\\\"]\\n\",\n    \"y = data[\\\"y\\\"].flatten()\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 12,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"[<matplotlib.lines.Line2D at 0x121d1b0f0>]\"\n      ]\n     },\n     \"execution_count\": 12,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"pos = np.where(y==1)[0]\\n\",\n    \"neg = np.where(y==0)[0]\\n\",\n    \"\\n\",\n    \"plt.plot(X[pos, 0], X[pos, 1], 'bx')\\n\",\n    \"plt.plot(X[neg, 0], X[neg, 1], 'yo')\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 13,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"SVC(C=1, cache_size=200, class_weight=None, coef0=0.0,\\n\",\n       \"  decision_function_shape='ovr', degree=3, gamma='auto_deprecated',\\n\",\n       \"  kernel=<function gaussian_wrapper.<locals>.gaussian_kernel at 0x121dda048>,\\n\",\n       \"  max_iter=-1, probability=False, random_state=None, shrinking=True,\\n\",\n       \"  tol=0.001, verbose=False)\"\n      ]\n     },\n     \"execution_count\": 13,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"clf = SVC(C=1, kernel = gaussian_wrapper(0.1))\\n\",\n    \"clf.fit(X, y)\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 14,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"[<matplotlib.lines.Line2D at 0x122955908>]\"\n      ]\n     },\n     \"execution_count\": 14,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"xp1 = np.array(np.linspace(np.min(X[:, 0]), np.max(X[:, 0]), 200))\\n\",\n    \"xp2 = np.array(np.linspace(np.min(X[:, 1]), np.max(X[:, 1]), 200))\\n\",\n    \"xp1_mesh, xp2_mesh = np.meshgrid(xp1, xp2)\\n\",\n    \"grid = np.array(list(zip(xp1_mesh.flatten(), xp2_mesh.flatten())))\\n\",\n    \"prediction_grid = clf.predict(grid).reshape((200, 200))\\n\",\n    \"plt.contour(xp1, xp2, prediction_grid)\\n\",\n    \"plt.plot(X[pos, 0], X[pos, 1], 'bx')\\n\",\n    \"plt.plot(X[neg, 0], X[neg, 1], 'yo')\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Dataset 3\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 15,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"data = sio.loadmat(\\\"ex6data3.mat\\\")\\n\",\n    \"X = data[\\\"X\\\"]\\n\",\n    \"y = data[\\\"y\\\"].flatten()\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 16,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"pos = np.where(y==1)[0]\\n\",\n    \"neg = np.where(y==0)[0]\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 17,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"SVC(C=2, cache_size=200, class_weight=None, coef0=0.0,\\n\",\n       \"  decision_function_shape='ovr', degree=3, gamma='auto_deprecated',\\n\",\n       \"  kernel=<function gaussian_wrapper.<locals>.gaussian_kernel at 0x12253b730>,\\n\",\n       \"  max_iter=-1, probability=False, random_state=None, shrinking=True,\\n\",\n       \"  tol=0.001, verbose=False)\"\n      ]\n     },\n     \"execution_count\": 17,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"clf = SVC(C=2, kernel = gaussian_wrapper(0.1))\\n\",\n    \"clf.fit(X, y)\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 18,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"[<matplotlib.lines.Line2D at 0x121bae6d8>]\"\n      ]\n     },\n     \"execution_count\": 18,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"xp1 = np.array(np.linspace(np.min(X[:, 0]), np.max(X[:, 0]), 200))\\n\",\n    \"xp2 = np.array(np.linspace(np.min(X[:, 1]), np.max(X[:, 1]), 200))\\n\",\n    \"xp1_mesh, xp2_mesh = np.meshgrid(xp1, xp2)\\n\",\n    \"grid = np.array(list(zip(xp1_mesh.flatten(), xp2_mesh.flatten())))\\n\",\n    \"prediction_grid = clf.predict(grid).reshape((200, 200))\\n\",\n    \"plt.contour(xp1, xp2, prediction_grid)\\n\",\n    \"plt.plot(X[pos, 0], X[pos, 1], 'bx')\\n\",\n    \"plt.plot(X[neg, 0], X[neg, 1], 'yo')\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Spam Classification\\n\",\n    \"---\\n\",\n    \"Many email services today provide spam filters that are able to classify emails into spam and non-spam email with high accuracy. In this part of the exercise, you will use SVMs to build your own spam filter.\\n\",\n    \"\\n\",\n    \"You will be training a classifier to classify whether a given email, x, is spam ($y = 1$) or non-spam ($y = 0$). In particular, you need to convert each email into a feature vector $x \\\\in \\\\mathbb{R}^n$. The following parts of the exercise will walk you through how such a feature vector can be constructed from an email.\\n\",\n    \"\\n\",\n    \"### Strategy\\n\",\n    \"Before starting on a machine learning task, it is usually insightful to take a look at examples from the dataset. Figure 8 shows a sample email that contains a URL, an email address (at the end), numbers, and dollar amounts. While many emails would contain similar types of entities (e.g., numbers, other URLs, or other email addresses), the specific entities (e.g., the specific URL or specific dollar amount) will be different in almost every email. Therefore, one method often employed in processing emails is to “normalize” these values, so that all URLs are treated the same, all numbers are treated the same, etc. For example, we could replace each URL in the email with the unique string “httpaddr” to indicate that a URL was present.\\n\",\n    \"\\n\",\n    \"This has the effect of letting the spam classifier make a classification decision based on whether any URL was present, rather than whether a specific URL was present. This typically improves the performance of a spam classifier, since spammers often randomize the URLs, and thus the odds of seeing any particular URL again in a new piece of spam is very small.\\n\",\n    \"\\n\",\n    \"### Preprocessing\\n\",\n    \"In `process_email.py`, I have implemented the following email preprocessing and normalization steps:\\n\",\n    \"- Lower-casing: The entire email is converted into lower case, so that captialization is ignored (e.g., IndIcaTE is treated the same as indicate).\\n\",\n    \"- Stripping HTML: All HTML tags are removed from the emails. Many emails often come with HTML formatting; we remove all the HTML tags, so that only the content remains.\\n\",\n    \"- Normalizing URLs: All URLs are replaced with the text “httpaddr”.\\n\",\n    \"- Normalizing Email Addresses: All email addresses are replaced\\n\",\n    \"with the text “emailaddr”.\\n\",\n    \"- Normalizing Numbers: All numbers are replaced with the text\\n\",\n    \"“number”.\\n\",\n    \"- Normalizing Dollars: All dollar signs ($) are replaced with the text\\n\",\n    \"“dollar”.\\n\",\n    \"- Word Stemming: Words are reduced to their stemmed form. For example, “discount”, “discounts”, “discounted” and “discounting” are all replaced with “discount”. Sometimes, the Stemmer actually strips off additional characters from the end, so “include”, “includes”, “included”, and “including” are all replaced with “includ”.\\n\",\n    \"- Removal of non-words: Non-words and punctuation have been removed. All white spaces (tabs, newlines, spaces) have all been trimmed to a single space character.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 19,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"[85, 915, 793, 1076, 882, 369, 1698, 789, 1821, 1830, 882, 430, 1170, 793, 1001, 1892, 1363, 591, 1675, 237, 161, 88, 687, 944, 1662, 1119, 1061, 1698, 374, 1161, 478, 1892, 1509, 798, 1181, 1236, 809, 1894, 1439, 1546, 180, 1698, 1757, 1895, 687, 1675, 991, 960, 1476, 70, 529, 1698, 530]\\n\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"from process_email import *\\n\",\n    \"\\n\",\n    \"# Demo of the process_email function. \\n\",\n    \"# Note: the indexes are all one lower than the exercise, because Python is 0-indexed where Octave is 1-indexed.\\n\",\n    \"with open('emailSample1.txt', 'r') as email:\\n\",\n    \"    email_contents = email.read()\\n\",\n    \"    tokens = process_email(email_contents)\\n\",\n    \"    print(tokens)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"You will now implement the feature extraction that converts each email into a vector in $\\\\mathbb{R}^n$. For this exercise, you will be using $n = \\\\#$ words in vocabulary list. Specifically, the feature $x_i \\\\in \\\\{0, 1\\\\}$ for an email corresponds to whether the i-th word in the dictionary occurs in the email. That is, $x_i = 1$ if the i-th word is in the email and $x_i = 0$ if the i-th word is not present in the email.\\n\",\n    \"Thus, for a typical email, this feature would look like:\\n\",\n    \"$$\\n\",\n    \"x = \\\\begin{bmatrix}\\n\",\n    \"0 \\\\\\\\\\n\",\n    \"\\\\vdots \\\\\\\\\\n\",\n    \"1 \\\\\\\\\\n\",\n    \"0 \\\\\\\\\\n\",\n    \"\\\\vdots \\\\\\\\\\n\",\n    \"1 \\\\\\\\\\n\",\n    \"0 \\\\\\\\\\n\",\n    \"\\\\vdots \\\\\\\\\\n\",\n    \"0\\n\",\n    \"\\\\end{bmatrix} \\\\in \\\\mathbb{R}^n\\n\",\n    \"$$.\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement `extract_features`.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 20,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def extract_features(tokens):\\n\",\n    \"    return np.zeros((1899, 1))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"The following code should return 45.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 21,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"0\"\n      ]\n     },\n     \"execution_count\": 21,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"features = extract_features(tokens)\\n\",\n    \"np.count_nonzero(features)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Training an SVM for spam classification\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 22,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"training_data = sio.loadmat(\\\"spamTrain.mat\\\")\\n\",\n    \"X = training_data[\\\"X\\\"]\\n\",\n    \"y = training_data[\\\"y\\\"].flatten()\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 23,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"SVC(C=0.1, cache_size=200, class_weight=None, coef0=0.0,\\n\",\n       \"  decision_function_shape='ovr', degree=3, gamma='auto_deprecated',\\n\",\n       \"  kernel='linear', max_iter=-1, probability=False, random_state=None,\\n\",\n       \"  shrinking=True, tol=0.001, verbose=False)\"\n      ]\n     },\n     \"execution_count\": 23,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"spam_predictor = SVC(C=0.1, kernel='linear')\\n\",\n    \"spam_predictor.fit(X, y)\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 24,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"'Training accuracy: 99.825000%'\"\n      ]\n     },\n     \"execution_count\": 24,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"predictions = spam_predictor.predict(X)\\n\",\n    \"'Training accuracy: {:2f}%'.format(np.mean(predictions == y) * 100)\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 25,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"'Test accuracy: 98.900000%'\"\n      ]\n     },\n     \"execution_count\": 25,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"testing_data = sio.loadmat(\\\"spamTest.mat\\\")\\n\",\n    \"X_test = testing_data[\\\"Xtest\\\"]\\n\",\n    \"y_test = testing_data[\\\"ytest\\\"].flatten()\\n\",\n    \"\\n\",\n    \"predictions = spam_predictor.predict(X_test)\\n\",\n    \"'Test accuracy: {:2f}%'.format(np.mean(predictions == y_test) * 100)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Top predictors\\n\",\n    \"\\n\",\n    \"To better understand how the spam classifier works, we can inspect the parameters to see which words the classifier thinks are the most predictive of spam.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 26,\n   \"metadata\": {\n    \"scrolled\": true\n   },\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/html\": [\n       \"<div>\\n\",\n       \"<style scoped>\\n\",\n       \"    .dataframe tbody tr th:only-of-type {\\n\",\n       \"        vertical-align: middle;\\n\",\n       \"    }\\n\",\n       \"\\n\",\n       \"    .dataframe tbody tr th {\\n\",\n       \"        vertical-align: top;\\n\",\n       \"    }\\n\",\n       \"\\n\",\n       \"    .dataframe thead th {\\n\",\n       \"        text-align: right;\\n\",\n       \"    }\\n\",\n       \"</style>\\n\",\n       \"<table border=\\\"1\\\" class=\\\"dataframe\\\">\\n\",\n       \"  <thead>\\n\",\n       \"    <tr style=\\\"text-align: right;\\\">\\n\",\n       \"      <th></th>\\n\",\n       \"      <th>vocabulary</th>\\n\",\n       \"      <th>weights</th>\\n\",\n       \"    </tr>\\n\",\n       \"  </thead>\\n\",\n       \"  <tbody>\\n\",\n       \"    <tr>\\n\",\n       \"      <th>1190</th>\\n\",\n       \"      <td>our</td>\\n\",\n       \"      <td>0.500614</td>\\n\",\n       \"    </tr>\\n\",\n       \"    <tr>\\n\",\n       \"      <th>297</th>\\n\",\n       \"      <td>click</td>\\n\",\n       \"      <td>0.465916</td>\\n\",\n       \"    </tr>\\n\",\n       \"    <tr>\\n\",\n       \"      <th>1397</th>\\n\",\n       \"      <td>remov</td>\\n\",\n       \"      <td>0.422869</td>\\n\",\n       \"    </tr>\\n\",\n       \"    <tr>\\n\",\n       \"      <th>738</th>\\n\",\n       \"      <td>guarante</td>\\n\",\n       \"      <td>0.383622</td>\\n\",\n       \"    </tr>\\n\",\n       \"    <tr>\\n\",\n       \"      <th>1795</th>\\n\",\n       \"      <td>visit</td>\\n\",\n       \"      <td>0.367710</td>\\n\",\n       \"    </tr>\\n\",\n       \"  </tbody>\\n\",\n       \"</table>\\n\",\n       \"</div>\"\n      ],\n      \"text/plain\": [\n       \"     vocabulary   weights\\n\",\n       \"1190        our  0.500614\\n\",\n       \"297       click  0.465916\\n\",\n       \"1397      remov  0.422869\\n\",\n       \"738    guarante  0.383622\\n\",\n       \"1795      visit  0.367710\"\n      ]\n     },\n     \"execution_count\": 26,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"weights = spam_predictor.coef_[0]\\n\",\n    \"df = pd.DataFrame({'vocabulary': vocabulary, 'weights': weights})\\n\",\n    \"df.sort_values(by='weights', ascending = False).head()\"\n   ]\n  }\n ],\n \"metadata\": {\n  \"kernelspec\": {\n   \"display_name\": \"Python 3\",\n   \"language\": \"python\",\n   \"name\": \"python3\"\n  },\n  \"language_info\": {\n   \"codemirror_mode\": {\n    \"name\": \"ipython\",\n    \"version\": 3\n   },\n   \"file_extension\": \".py\",\n   \"mimetype\": \"text/x-python\",\n   \"name\": \"python\",\n   \"nbconvert_exporter\": \"python\",\n   \"pygments_lexer\": \"ipython3\",\n   \"version\": \"3.7.1\"\n  }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n"
  },
  {
    "path": "ex6/emailSample1.txt",
    "content": "> Anyone knows how much it costs to host a web portal ?\n>\nWell, it depends on how many visitors you're expecting.\nThis can be anywhere from less than 10 bucks a month to a couple of $100. \nYou should checkout http://www.rackspace.com/ or perhaps Amazon EC2 \nif youre running something big..\n\nTo unsubscribe yourself from this mailing list, send an email to:\ngroupname-unsubscribe@egroups.com\n\n"
  },
  {
    "path": "ex6/process_email.py",
    "content": "import re\nfrom nltk.stem import PorterStemmer\n    \n# Load vocabulary\nvocabulary = []\nwith open('vocab.txt', 'r') as f:\n    lines = f.readlines()\n    vocabulary = [line[:-1] for line in lines]\n\ndef process_email(email_contents):\n    \"\"\" preprocesses a the body of an email and returns a list of word_indices \"\"\"\n    global vocabulary\n\n    # ----- Preprocess email -----\n\n    # Lower case\n    email_contents = email_contents.lower()\n\n    # Remove all HTML\n    html = re.compile(r'<[^<>]+>')\n    email_contents = html.sub('', email_contents)\n\n    # Handle numbers\n    numbers = re.compile(r'[0-9]+')\n    email_contents = numbers.sub('number', email_contents)\n\n    # Handle URLs\n    urls = re.compile(r'(http|https)://[^\\s]*')\n    email_contents = urls.sub('httpaddr', email_contents)\n\n    # Email\n    email_addresses = re.compile(r'[^\\s]+@[^\\s]+')\n    email_contents = email_addresses.sub('emailaddr', email_contents)\n\n    # Dollar sign\n    dollar_sign = re.compile(r'[$]+')\n    email_contents = dollar_sign.sub('dollar', email_contents)\n\n    # ----- Tokenize email -----\n    tokens = []\n    words = re.split(r\"\\s|\\@|\\$|\\/|\\#|\\.|\\-|\\:|\\&|\\*|\\+|\\=|\\[|\\]|\\?|\\!|\\(|\\)|\\{|\\}|\\,|\\'|\\'|\\\"|\\>|\\_|\\<|\\;|\\%\", email_contents)\n\n    stemmer = PorterStemmer()\n\n    for word in words:\n        # Remove nonalphanumeric characters\n        alphanumeric = re.compile(r'[^a-zA-Z0-9]')\n        word = alphanumeric.sub('', word)\n\n        # Stem the word\n        word = stemmer.stem(word)\n\n        # Get index if it exists\n        if word in vocabulary:\n            tokens.append(vocabulary.index(word))\n \n    return tokens\n\nif __name__ == '__main__':\n    # Run a test.\n    # Note: the indexes are all 1 lower than the exercise, because Python is 0-indexed.\n    with open('emailSample1.txt', 'r') as email:\n        email_contents = email.read()\n        tokens = process_email(email_contents)\n        print(tokens)\n"
  },
  {
    "path": "ex6/vocab.txt",
    "content": "aa\nab\nabil\nabl\nabout\nabov\nabsolut\nabus\nac\naccept\naccess\naccord\naccount\nachiev\nacquir\nacross\nact\naction\nactiv\nactual\nad\nadam\nadd\naddit\naddress\nadministr\nadult\nadvanc\nadvantag\nadvertis\nadvic\nadvis\nae\naf\naffect\naffili\nafford\nafrica\nafter\nag\nagain\nagainst\nagenc\nagent\nago\nagre\nagreement\naid\nair\nal\nalb\nalign\nall\nallow\nalmost\nalon\nalong\nalreadi\nalsa\nalso\naltern\nalthough\nalwai\nam\namaz\namerica\namerican\namong\namount\namp\nan\nanalysi\nanalyst\nand\nani\nanim\nannounc\nannual\nannuiti\nanoth\nanswer\nanti\nanumb\nanybodi\nanymor\nanyon\nanyth\nanywai\nanywher\naol\nap\napolog\napp\nappar\nappear\nappl\nappli\napplic\nappreci\napproach\napprov\napt\nar\narchiv\narea\naren\nargument\narial\narm\naround\narrai\narriv\nart\narticl\nartist\nas\nascii\nask\nasset\nassist\nassoci\nassum\nassur\nat\natol\nattach\nattack\nattempt\nattent\nattornei\nattract\naudio\naug\naugust\nauthor\nauto\nautom\nautomat\navail\naverag\navoid\nawai\nawar\naward\nba\nbabi\nback\nbackground\nbackup\nbad\nbalanc\nban\nbank\nbar\nbase\nbasenumb\nbasi\nbasic\nbb\nbc\nbd\nbe\nbeat\nbeberg\nbecaus\nbecom\nbeen\nbefor\nbegin\nbehalf\nbehavior\nbehind\nbeliev\nbelow\nbenefit\nbest\nbeta\nbetter\nbetween\nbf\nbig\nbill\nbillion\nbin\nbinari\nbit\nblack\nblank\nblock\nblog\nblood\nblue\nbnumber\nboard\nbodi\nboi\nbonu\nbook\nboot\nborder\nboss\nboston\nbotan\nboth\nbottl\nbottom\nboundari\nbox\nbrain\nbrand\nbreak\nbrian\nbring\nbroadcast\nbroker\nbrowser\nbug\nbui\nbuild\nbuilt\nbulk\nburn\nbush\nbusi\nbut\nbutton\nby\nbyte\nca\ncabl\ncach\ncalcul\ncalifornia\ncall\ncame\ncamera\ncampaign\ncan\ncanada\ncannot\ncanon\ncapabl\ncapillari\ncapit\ncar\ncard\ncare\ncareer\ncarri\ncartridg\ncase\ncash\ncat\ncatch\ncategori\ncaus\ncb\ncc\ncd\nce\ncell\ncent\ncenter\ncentral\ncenturi\nceo\ncertain\ncertainli\ncf\nchalleng\nchanc\nchang\nchannel\nchar\ncharact\ncharg\ncharset\nchat\ncheap\ncheck\ncheer\nchief\nchildren\nchina\nchip\nchoic\nchoos\nchri\nciti\ncitizen\ncivil\nclaim\nclass\nclassifi\nclean\nclear\nclearli\nclick\nclient\nclose\nclue\ncnet\ncnumber\nco\ncode\ncollect\ncolleg\ncolor\ncom\ncombin\ncome\ncomfort\ncommand\ncomment\ncommentari\ncommerci\ncommiss\ncommit\ncommon\ncommun\ncompani\ncompar\ncomparison\ncompat\ncompet\ncompetit\ncompil\ncomplet\ncomprehens\ncomput\nconcentr\nconcept\nconcern\ncondit\nconf\nconfer\nconfid\nconfidenti\nconfig\nconfigur\nconfirm\nconflict\nconfus\ncongress\nconnect\nconsid\nconsolid\nconstitut\nconstruct\nconsult\nconsum\ncontact\ncontain\ncontent\ncontinu\ncontract\ncontribut\ncontrol\nconveni\nconvers\nconvert\ncool\ncooper\ncopi\ncopyright\ncore\ncorpor\ncorrect\ncorrespond\ncost\ncould\ncouldn\ncount\ncountri\ncoupl\ncours\ncourt\ncover\ncoverag\ncrash\ncreat\ncreativ\ncredit\ncritic\ncross\ncultur\ncurrent\ncustom\ncut\ncv\nda\ndagga\ndai\ndaili\ndan\ndanger\ndark\ndata\ndatabas\ndatapow\ndate\ndave\ndavid\ndc\nde\ndead\ndeal\ndear\ndeath\ndebt\ndecad\ndecid\ndecis\ndeclar\ndeclin\ndecor\ndefault\ndefend\ndefens\ndefin\ndefinit\ndegre\ndelai\ndelet\ndeliv\ndeliveri\ndell\ndemand\ndemocrat\ndepart\ndepend\ndeposit\ndescrib\ndescript\ndeserv\ndesign\ndesir\ndesktop\ndespit\ndetail\ndetect\ndetermin\ndev\ndevel\ndevelop\ndevic\ndi\ndial\ndid\ndidn\ndiet\ndiffer\ndifficult\ndigit\ndirect\ndirectli\ndirector\ndirectori\ndisabl\ndiscount\ndiscov\ndiscoveri\ndiscuss\ndisk\ndisplai\ndisposit\ndistanc\ndistribut\ndn\ndnumber\ndo\ndoc\ndocument\ndoe\ndoer\ndoesn\ndollar\ndollarac\ndollarnumb\ndomain\ndon\ndone\ndont\ndoubl\ndoubt\ndown\ndownload\ndr\ndraw\ndream\ndrive\ndriver\ndrop\ndrug\ndue\ndure\ndvd\ndw\ndynam\nea\neach\nearli\nearlier\nearn\nearth\neasi\neasier\neasili\neat\neb\nebai\nec\necho\neconom\neconomi\ned\nedg\nedit\neditor\neduc\neff\neffect\neffici\neffort\neither\nel\nelectron\nelimin\nels\nemail\nemailaddr\nemerg\nempir\nemploy\nemploye\nen\nenabl\nencod\nencourag\nend\nenemi\nenenkio\nenergi\nengin\nenglish\nenhanc\nenjoi\nenough\nensur\nenter\nenterpris\nentertain\nentir\nentri\nenumb\nenviron\nequal\nequip\nequival\nerror\nespeci\nessenti\nestablish\nestat\nestim\net\netc\neuro\neurop\neuropean\neven\nevent\neventu\never\neveri\neveryon\neveryth\nevid\nevil\nexactli\nexampl\nexcel\nexcept\nexchang\nexcit\nexclus\nexecut\nexercis\nexist\nexmh\nexpand\nexpect\nexpens\nexperi\nexpert\nexpir\nexplain\nexplor\nexpress\nextend\nextens\nextra\nextract\nextrem\ney\nfa\nface\nfact\nfactor\nfail\nfair\nfall\nfals\nfamili\nfaq\nfar\nfast\nfaster\nfastest\nfat\nfather\nfavorit\nfax\nfb\nfd\nfeatur\nfeder\nfee\nfeed\nfeedback\nfeel\nfemal\nfew\nffffff\nffnumber\nfield\nfight\nfigur\nfile\nfill\nfilm\nfilter\nfinal\nfinanc\nfinanci\nfind\nfine\nfinish\nfire\nfirewal\nfirm\nfirst\nfit\nfive\nfix\nflag\nflash\nflow\nfnumber\nfocu\nfolder\nfolk\nfollow\nfont\nfood\nfor\nforc\nforeign\nforev\nforget\nfork\nform\nformat\nformer\nfortun\nforward\nfound\nfoundat\nfour\nfranc\nfree\nfreedom\nfrench\nfreshrpm\nfri\nfridai\nfriend\nfrom\nfront\nftoc\nftp\nfull\nfulli\nfun\nfunction\nfund\nfurther\nfutur\nga\ngain\ngame\ngari\ngarrigu\ngave\ngcc\ngeek\ngener\nget\ngif\ngift\ngirl\ngive\ngiven\nglobal\ngnome\ngnu\ngnupg\ngo\ngoal\ngod\ngoe\ngold\ngone\ngood\ngoogl\ngot\ngovern\ngpl\ngrand\ngrant\ngraphic\ngreat\ngreater\nground\ngroup\ngrow\ngrowth\ngt\nguarante\nguess\ngui\nguid\nha\nhack\nhad\nhalf\nham\nhand\nhandl\nhappen\nhappi\nhard\nhardwar\nhat\nhate\nhave\nhaven\nhe\nhead\nheader\nheadlin\nhealth\nhear\nheard\nheart\nheaven\nhei\nheight\nheld\nhello\nhelp\nhelvetica\nher\nherba\nhere\nhermio\nhettinga\nhi\nhigh\nhigher\nhighli\nhighlight\nhim\nhistori\nhit\nhold\nhome\nhonor\nhope\nhost\nhot\nhour\nhous\nhow\nhowev\nhp\nhtml\nhttp\nhttpaddr\nhuge\nhuman\nhundr\nibm\nid\nidea\nident\nidentifi\nidnumb\nie\nif\nignor\nii\niii\niiiiiiihnumberjnumberhnumberjnumberhnumb\nilleg\nim\nimag\nimagin\nimmedi\nimpact\nimplement\nimport\nimpress\nimprov\nin\ninc\ninclud\nincom\nincreas\nincred\ninde\nindepend\nindex\nindia\nindian\nindic\nindividu\nindustri\ninfo\ninform\niniti\ninlin\ninnov\ninput\ninsert\ninsid\ninstal\ninstanc\ninstant\ninstead\ninstitut\ninstruct\ninsur\nint\nintegr\nintel\nintellig\nintend\ninteract\ninterest\ninterfac\nintern\ninternet\ninterview\ninto\nintro\nintroduc\ninumb\ninvest\ninvestig\ninvestor\ninvok\ninvolv\nip\nireland\nirish\nis\nisland\nisn\niso\nisp\nissu\nit\nitem\nitself\njabber\njame\njava\njim\njnumberiiiiiiihepihepihf\njob\njoe\njohn\njoin\njournal\njudg\njudgment\njul\njuli\njump\njune\njust\njustin\nkeep\nkei\nkept\nkernel\nkevin\nkeyboard\nkid\nkill\nkind\nking\nkingdom\nknew\nknow\nknowledg\nknown\nla\nlack\nland\nlanguag\nlaptop\nlarg\nlarger\nlargest\nlaser\nlast\nlate\nlater\nlatest\nlaunch\nlaw\nlawrenc\nle\nlead\nleader\nlearn\nleast\nleav\nleft\nlegal\nlender\nlength\nless\nlesson\nlet\nletter\nlevel\nlib\nlibrari\nlicens\nlife\nlifetim\nlight\nlike\nlimit\nline\nlink\nlinux\nlist\nlisten\nlittl\nlive\nll\nlo\nload\nloan\nlocal\nlocat\nlock\nlockergnom\nlog\nlong\nlonger\nlook\nlose\nloss\nlost\nlot\nlove\nlow\nlower\nlowest\nlt\nma\nmac\nmachin\nmade\nmagazin\nmai\nmail\nmailer\nmain\nmaintain\nmajor\nmake\nmaker\nmale\nman\nmanag\nmani\nmanual\nmanufactur\nmap\nmarch\nmargin\nmark\nmarket\nmarshal\nmass\nmaster\nmatch\nmateri\nmatter\nmatthia\nmayb\nme\nmean\nmeasur\nmechan\nmedia\nmedic\nmeet\nmember\nmembership\nmemori\nmen\nmention\nmenu\nmerchant\nmessag\nmethod\nmh\nmichael\nmicrosoft\nmiddl\nmight\nmike\nmile\nmilitari\nmillion\nmime\nmind\nmine\nmini\nminimum\nminut\nmiss\nmistak\nmobil\nmode\nmodel\nmodem\nmodifi\nmodul\nmoment\nmon\nmondai\nmonei\nmonitor\nmonth\nmonthli\nmore\nmorn\nmortgag\nmost\nmostli\nmother\nmotiv\nmove\nmovi\nmpnumber\nmr\nms\nmsg\nmuch\nmulti\nmultipart\nmultipl\nmurphi\nmusic\nmust\nmy\nmyself\nname\nnation\nnatur\nnbsp\nnear\nnearli\nnecessari\nneed\nneg\nnet\nnetscap\nnetwork\nnever\nnew\nnewslett\nnext\nnextpart\nnice\nnigeria\nnight\nno\nnobodi\nnon\nnone\nnor\nnormal\nnorth\nnot\nnote\nnoth\nnotic\nnow\nnt\nnull\nnumber\nnumbera\nnumberam\nnumberanumb\nnumberb\nnumberbit\nnumberc\nnumbercb\nnumbercbr\nnumbercfont\nnumbercli\nnumbercnumb\nnumbercp\nnumberctd\nnumberd\nnumberdari\nnumberdnumb\nnumberenumb\nnumberf\nnumberfb\nnumberff\nnumberffont\nnumberfp\nnumberftd\nnumberk\nnumberm\nnumbermb\nnumberp\nnumberpd\nnumberpm\nnumberpx\nnumberst\nnumberth\nnumbertnumb\nnumberx\nobject\noblig\nobtain\nobvious\noccur\noct\noctob\nof\noff\noffer\noffic\noffici\noften\noh\nok\nold\non\nonc\nonli\nonlin\nopen\noper\nopinion\nopportun\nopt\noptim\noption\nor\norder\norg\norgan\norigin\nos\nosdn\nother\notherwis\nour\nout\noutlook\noutput\noutsid\nover\nown\nowner\noz\npacif\npack\npackag\npage\npai\npaid\npain\npalm\npanel\npaper\nparagraph\nparent\npart\nparti\nparticip\nparticular\nparticularli\npartit\npartner\npass\npassword\npast\npatch\npatent\npath\npattern\npaul\npayment\npc\npeac\npeopl\nper\npercent\npercentag\nperfect\nperfectli\nperform\nperhap\nperiod\nperl\nperman\npermiss\nperson\npgp\nphone\nphoto\nphp\nphrase\nphysic\npick\npictur\npiec\npiiiiiiii\npipe\npjnumber\nplace\nplai\nplain\nplan\nplanet\nplant\nplanta\nplatform\nplayer\npleas\nplu\nplug\npm\npocket\npoint\npolic\npolici\npolit\npoor\npop\npopul\npopular\nport\nposit\npossibl\npost\npotenti\npound\npowel\npower\npowershot\npractic\npre\npredict\nprefer\npremium\nprepar\npresent\npresid\npress\npretti\nprevent\npreviou\nprevious\nprice\nprincipl\nprint\nprintabl\nprinter\nprivaci\nprivat\nprize\npro\nprobabl\nproblem\nprocedur\nprocess\nprocessor\nprocmail\nproduc\nproduct\nprofession\nprofil\nprofit\nprogram\nprogramm\nprogress\nproject\npromis\npromot\nprompt\nproperti\npropos\nproprietari\nprospect\nprotect\nprotocol\nprove\nproven\nprovid\nproxi\npub\npublic\npublish\npudg\npull\npurchas\npurpos\nput\npython\nqnumber\nqualifi\nqualiti\nquarter\nquestion\nquick\nquickli\nquit\nquot\nradio\nragga\nrais\nrandom\nrang\nrate\nrather\nratio\nrazor\nrazornumb\nre\nreach\nread\nreader\nreadi\nreal\nrealiz\nrealli\nreason\nreceiv\nrecent\nrecipi\nrecommend\nrecord\nred\nredhat\nreduc\nrefer\nrefin\nreg\nregard\nregion\nregist\nregul\nregular\nrel\nrelat\nrelationship\nreleas\nrelev\nreliabl\nremain\nrememb\nremot\nremov\nreplac\nrepli\nreport\nrepositori\nrepres\nrepubl\nrequest\nrequir\nresearch\nreserv\nresid\nresourc\nrespect\nrespond\nrespons\nrest\nresult\nretail\nreturn\nreveal\nrevenu\nrevers\nreview\nrevok\nrh\nrich\nright\nrisk\nroad\nrobert\nrock\nrole\nroll\nrom\nroman\nroom\nroot\nround\nrpm\nrss\nrule\nrun\nsa\nsafe\nsai\nsaid\nsale\nsame\nsampl\nsan\nsaou\nsat\nsatellit\nsave\nsaw\nscan\nschedul\nschool\nscienc\nscore\nscreen\nscript\nse\nsearch\nseason\nsecond\nsecret\nsection\nsecur\nsee\nseed\nseek\nseem\nseen\nselect\nself\nsell\nseminar\nsend\nsender\nsendmail\nsenior\nsens\nsensit\nsent\nsep\nsepar\nseptemb\nsequenc\nseri\nserif\nseriou\nserv\nserver\nservic\nset\nsetup\nseven\nseventh\nsever\nsex\nsexual\nsf\nshape\nshare\nshe\nshell\nship\nshop\nshort\nshot\nshould\nshow\nside\nsign\nsignatur\nsignific\nsimilar\nsimpl\nsimpli\nsinc\nsincer\nsingl\nsit\nsite\nsituat\nsix\nsize\nskeptic\nskill\nskin\nskip\nsleep\nslow\nsmall\nsmart\nsmoke\nsmtp\nsnumber\nso\nsocial\nsocieti\nsoftwar\nsold\nsolut\nsolv\nsome\nsomeon\nsometh\nsometim\nson\nsong\nsoni\nsoon\nsorri\nsort\nsound\nsourc\nsouth\nspace\nspain\nspam\nspamassassin\nspamd\nspammer\nspeak\nspec\nspecial\nspecif\nspecifi\nspeech\nspeed\nspend\nsponsor\nsport\nspot\nsrc\nssh\nst\nstabl\nstaff\nstai\nstand\nstandard\nstar\nstart\nstate\nstatement\nstatu\nstep\nsteve\nstill\nstock\nstop\nstorag\nstore\nstori\nstrategi\nstream\nstreet\nstring\nstrip\nstrong\nstructur\nstudi\nstuff\nstupid\nstyle\nsubject\nsubmit\nsubscrib\nsubscript\nsubstanti\nsuccess\nsuch\nsuffer\nsuggest\nsuit\nsum\nsummari\nsummer\nsun\nsuper\nsuppli\nsupport\nsuppos\nsure\nsurpris\nsuse\nsuspect\nsweet\nswitch\nsystem\ntab\ntabl\ntablet\ntag\ntake\ntaken\ntalk\ntape\ntarget\ntask\ntax\nteach\nteam\ntech\ntechnic\ntechniqu\ntechnolog\ntel\ntelecom\ntelephon\ntell\ntemperatur\ntempl\nten\nterm\ntermin\nterror\nterrorist\ntest\ntexa\ntext\nthan\nthank\nthat\nthe\nthei\ntheir\nthem\nthemselv\nthen\ntheori\nthere\ntherefor\nthese\nthi\nthing\nthink\nthinkgeek\nthird\nthose\nthough\nthought\nthousand\nthread\nthreat\nthree\nthrough\nthu\nthursdai\nti\nticket\ntim\ntime\ntip\ntire\ntitl\ntm\nto\ntodai\ntogeth\ntoken\ntold\ntoll\ntom\ntoner\ntoni\ntoo\ntook\ntool\ntop\ntopic\ntotal\ntouch\ntoward\ntrack\ntrade\ntradit\ntraffic\ntrain\ntransact\ntransfer\ntravel\ntreat\ntree\ntri\ntrial\ntrick\ntrip\ntroubl\ntrue\ntruli\ntrust\ntruth\ntry\ntue\ntuesdai\nturn\ntv\ntwo\ntype\nuk\nultim\nun\nunder\nunderstand\nunfortun\nuniqu\nunison\nunit\nunivers\nunix\nunless\nunlik\nunlimit\nunseen\nunsolicit\nunsubscrib\nuntil\nup\nupdat\nupgrad\nupon\nurgent\nurl\nus\nusa\nusag\nusb\nusd\nusdollarnumb\nuseless\nuser\nusr\nusual\nutil\nvacat\nvalid\nvalu\nvaluabl\nvar\nvariabl\nvarieti\nvariou\nve\nvendor\nventur\nveri\nverifi\nversion\nvia\nvideo\nview\nvirtual\nvisa\nvisit\nvisual\nvnumber\nvoic\nvote\nvs\nvulner\nwa\nwai\nwait\nwake\nwalk\nwall\nwant\nwar\nwarm\nwarn\nwarranti\nwashington\nwasn\nwast\nwatch\nwater\nwe\nwealth\nweapon\nweb\nweblog\nwebsit\nwed\nwednesdai\nweek\nweekli\nweight\nwelcom\nwell\nwent\nwere\nwest\nwhat\nwhatev\nwhen\nwhere\nwhether\nwhich\nwhile\nwhite\nwhitelist\nwho\nwhole\nwhose\nwhy\nwi\nwide\nwidth\nwife\nwill\nwilliam\nwin\nwindow\nwing\nwinner\nwireless\nwish\nwith\nwithin\nwithout\nwnumberp\nwoman\nwomen\nwon\nwonder\nword\nwork\nworker\nworld\nworldwid\nworri\nworst\nworth\nwould\nwouldn\nwrite\nwritten\nwrong\nwrote\nwww\nximian\nxml\nxp\nyahoo\nye\nyeah\nyear\nyesterdai\nyet\nyork\nyou\nyoung\nyour\nyourself\nzdnet\nzero\nzip\n"
  },
  {
    "path": "ex7/K-means Clustering and Principal Component Analysis (Exercises).ipynb",
    "content": "{\n \"cells\": [\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"# K-means Clustering and Principal Component Analysis\\n\",\n    \"\\n\",\n    \"Stanford CS229 - Machine Learning by Andrew Ng. Programming exercise 7.\\n\",\n    \"\\n\",\n    \"Please check out [the repository on GitHub](https://github.com/rickwierenga/CS229-Python/). If you spot any mistakes or inconcistencies, please create an issue. For questions you can find me on Twitter: [@rickwierenga](https://twitter.com/rickwierenga). Starring the project on GitHub means a ton to me!\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 1,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"import numpy as np\\n\",\n    \"import matplotlib.pylab as plt\\n\",\n    \"import scipy.io as sio\\n\",\n    \"%matplotlib inline\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## _K_-means Clustering\\n\",\n    \"---\\n\",\n    \"The K-means algorithm is a method to automatically cluster similar data examples together. Concretely, you are given a training set $\\\\{x^{(1)},...,x^{(m)}\\\\}$ (where $x^{(i)} \\\\in \\\\mathbb{R}^n$), and want to group the data into a few cohesive “clusters”. The intuition behind _K_-means is an iterative procedure that starts by guessing the initial centroids, and then refines this guess by repeatedly assigning examples to their closest centroids and then recomputing the centroids based on the assignments.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 2,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"[<matplotlib.lines.Line2D at 0x129824a90>]\"\n      ]\n     },\n     \"execution_count\": 2,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"iVBORw0KGgoAAAANSUhEUgAAAW4AAAD8CAYAAABXe05zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvDW2N/gAAIABJREFUeJztnXGMXNd13r+zw5E4S7ka2mYDayyarFFQML01N95YdFgEEd2abmSxCzqNqtABmj8qoGhTi1E3WBVESQJCyYJNZAMtArB2UgRUVcqSupBM17QBMgjMlrSX3mVoWmSRWBapkQOvI61siyNxuHv6x+wbvnlz73v3vXlv5r3Z7wcY5s7OvDnzVvPdc7977rmiqiCEEFIcRgYdACGEkHhQuAkhpGBQuAkhpGBQuAkhpGBQuAkhpGBQuAkhpGBQuAkhpGBQuAkhpGA4CbeIVEXkORG5IiIvi8gnsw6MEEKImTWOz/sSgG+o6m+KyB0ARsOe/P73v183bdrUa2yEELJquHDhwk9VdYPLcyOFW0TuBvBrAP4FAKjqTQA3w16zadMmzM7Ourw/IYQQACLyqutzXaySzQAWAPypiMyJyJdFZF3i6AghhPSEi3CvAfDLAP5YVccBvA1gOvgkEXlURGZFZHZhYSHlMAkhhHi4CPdrAF5T1fMrPz+HlpB3oKrHVHVCVSc2bHCyaQghhCQgUrhV9W8AXBeRLSsPfQrADzKNihBCiBXXqpLfA/D0SkXJDwH8bnYhEUIICcNJuFV1HsBExrGQVcbMXB1HT13F64sN3FOtYGrXFkyO1wYdFiG5xzXjJiRVZubqeOKFS2g0lwAA9cUGnnjhEgBQvAmJIDfCzexrdXH01NW2aHs0mks4euoq/+6ERJAL4S5a9sVBpndeX2zEepwQcptcNJkKy77yhjfI1BcbUNweZGbm6oMOrVDcU63EepwQcptcCHeRsq8iDTJ5ZmrXFlTKpY7HKuUSpnZtsbyCEOKRC6vknmoFdYNI5zH7yvsgUxQbx4upCLESkjdykXEXKfvK8xS/KDbOzFwdO46cxr4T8wCAvds3AgD2nZjHjiOncxcvIXkjFxl3kbKvB+7bgOPnrhkfHwT+DHtEBEuqHb/PW6WGaSHafz/zvjBNSB7IhXADrS9pml/UrCyDM1fMDbRsj2dJUASDou2RpY0T9z6b1giC5G2wISRv5Ea40yTL8sI8edwuIghkZ+Mkuc+u9ykvawZpUpT1B5J/cuFxp02WlR958rhdxC3LtYIk99n1PuVhzSBNirL+QIrBUAp3lllxnhZSbeJWEoEAqFUr+NzHazh66io2T5/EjiOnsX/mEnYcOd3+uRfhSHKfTfcvSF4XpnuBZaQkTYZSuLPMiifHazi8Zwy1aqUtjof3jA1kymsbRP7wtz6GV448iKldW/D8hXpHlnf83LXUsr4k99l0/z6/fWMu7meW5MliI8VnKD3uqV1bOrxXIN0sLu2F1F7iAOzVOFkvBCa9z3m5f/2kSHsVSP4ZSuEuUnmhC2GLWmEiaBIKE0mzvmG7z1mSdTJBVhdDKdzA8GR1SStkZubqEADmAsFOesn6srrPw1aBwUGOpMlQCHcRvuRJY0za/vToqatOop3HrK9o3SJdGZZkggyewi9OFqHMqpcYky5qudgfeV0IZAUGIeEUPuOOykjjZLpZZe62GB9/9iIAexY5M1c3bmMHou0N22KYx/rRMs5O7wy9xqDuHSswCAmn8MId9iWPM+UexG7LJdXIeEyiHWVvzMzVcePmrdCY3rzRDP296X48dmIeh166jAMPbe2IN+zeAfF9XVZgEBJO4a2SsFriOFPuNKbnXte74OaWMMGJEw/Q2lwTZm94IholzFHY3v/NG03sOzGP/TOXQp/baC7h4IuXE1lEedrkREgeKbxwh33J40y5e52eh/nYUbsF48SzrNpzEycAqFbKob8Ps1kUwNPnrrUF2BbrYqOZaDDM0yYnQvJI4a2SsDKro6euGgVoRASbp092PLfX6XlYxu55yY8/ezHSr/a8YltFyN2VMnYcOW21HlwGmvKI4ODuraHPKVm8dQ8F2usIUX56EJcYWYFBiJ3CCzdg/5KbNj0At9uf+r3YXjdIRGXsXnxh7xH0ioOURwRv37yFxUazK37v+i4ievSffSxSFMNE26O+2MCOI6dRX2x01YxXyiWsLY8YLRt61YT0RuGtkjCCU+6SSNdz/BUovUzPXfp2RL1HmM1Rq1Zw19o1aC6ZD0rwiLJlatWKcSE06M3XHMRVcNtS0ZWfgdZ99j5HeaTznvfTq7atORBSdEQdMqu4TExM6OzsbOrX7ZXN0yeNFoQAeOXIgz1d25QtV8olo/jbSuei4nONf2aujkMvXe7Kdsslwbo71uCtRrP9voB5FvC5j9fw/IW6dSCx7coMPm56z35YIHH+HoTkARG5oKoTTs91EW4R+RGAnwNYAnAr6uJ5FW5vWh+kJII//K1o+8CPSXyB6NI3k6B44uZZIEFq1QrOTu+0xl+tlDF/4NOhMVZHy/jFO7fQXL799w6zM2or8ftfr4q2AMfxtL34+4ntXg0iFkJciCPccTzuB1T1pwljygVhnnecmm1T3fK+E/PYu31jpCgcfPFy1/s3l9Qq2n5rYWrXFkx99WKH+ALAz95pYmauHhr7zxq3jOdR2jLq+mIjdIHQJoy2awUXg7Mmqr4/7y0SCAljqD3uIJ7HHOZ1u2DyooMlciZm5upWgTYR9MAnx2sol7pjX9bWgBB8L395ostiox/TPfJj8tLDXuGVSE49dxHbDn0zc9/ZtuZQHS3nvkUCIVG4CrcC+KaIXBCRR7MMKGsmx2tY7vFQXdvzvBI5P/4FMm+LuwsC4Oz0zq5M8EZz2fj84IDgWs9tI0roTQute7dvjDzdxptdeKK578Q8NmUg4rb6flWwDwopPK5WyT9U1bqI/F0A3xKRK6r6F/4nrAj6owCwcePGlMNMl+pouacytTCP1y/qrqew296jF3rt6+FVlcTtBT7xofe2n+/yab3npN0B0Fbfv+/EvPH57INCioSTcKtqfeX/fyIi/wvAJwD8ReA5xwAcA1qLkynH2TOeANkEt1wS5zI1TwBMH9IvuEmzXgHwwH0bjL9bbxl0RNDhc8ddQPTj+epJ+rf4xTyODw70dhpPVCwetv8GWFtOikSkVSIi60TkPd6/AXwawPezDixN/H6vjXV3tMYwl7rfyfEa9m7f2OXpBmuUXU9h3/Hh93ZcSwE8f6FufP8DD201+tyq6PBqXQ7lNeH31Xvt35IkhqwzX/ZBIcOAi8f9SwC+LSIXAXwHwElV/Ua2YaWLS+a72GjGWrR6cnIMe7dvbC/ilUTwuY93Zngup7Af3jOGH/1tt63gtX0Nvv/keA0P/8q9xuv6RdXzoNePhvck8aiUS/jiw9s6fPVe+rd4M5xGc6l9j9aPlrs25ATJOvNlHxQyDERaJar6QwAf60MsmeEiNP7dfh5hU/eZuTqev1Bv+9ZLqnj+Qh0TH3pv+/m2bfRBobD5rrYyxTNXFqyfw/9Zvaw5qlNgzeddR1lKQLS4zszVO8oWl1RRHhEceGgrZl99A8fPXTO+ToC+ZL6roQ8KSx6Hm6HoVRJFlN9bKZesGblN9F2OFHM9Z9C2WGq6ZlhMQOuz+r+0YYsN5ZLg6G/e3ngU1SsFcLMVDr54uavWvLmsOPjiZay70/6fnKLYR5PlhWE9+o3cZuiF23aogLc1279DMM6ilauNEJXdzczV8Yt3wg89CF7TNhB5i5pR4utx151rsO/EPI6eutq+B2Gvi+oF7mGrVV9sNPFWSB27S3+UKJhpJj+nlBSHwgq3yxfUlkFWK2Uc3L216/lxugOmdUrL0VNXu7LTqGuaLBgBsHf7Rpy5shAp2uURAeT2KTheRhb1uqhe4C6EDTq92iTMNFvw6Lfhp5A7J10P37VlkOvuXNP1RY67aGWrTtj0vgo+/MTXsWn6JD78xNc7TooxEfVlMg0eplifengbnpwcC72e91xbl8Go3ZKug5JtQXS0PGLdcbl3+8aexZWHDLdw6VRJik0hM27XqWDczCPOopXJv970vgrO/vUb7ecsqbYX4p6cHDNeJ8x/r4VM9W2x2vzy9aNlzP2HViOqzdMnje+3pGr1++OUzB14aCt+/9l5BCcS3szi8J6xTOwMZpoteu0tT/JPITNu1y9ovzOP//PDN4yPP3P+uvU1cXt+RGHbnOl/3Pb5vVmG5zV7GXjckrnJ8RruNhyN1lzS9uB6dnonXjnyoHFbf1KYabZgyePwU8iM29VfzjLzMPmpNsK2uvsz9+BJMl4vj8dOzHdk3/tnLuGZ89expIqSCB65/952Rm9b/PMen5mr4+13uxdDvfvSS6mcSzVLltkvM83brIaSx9VMITNu191vWWYecbez+/334MksQKuhVK1a6RK8YC+Pvf/t/+L4uWsd9ePHz11re+lhWac32ASrPtaPlnu+L8F1BxtZZr/MNMlqoZAZt2t9tPfcLL64cTNHr7rB+7ep8iHqmo3mUoeH7ueZ89fx5ORYaNZpG2xG7+herI2Ly0DWj+yXmSZZDRRSuIHBf0Ftds1oecTYetVf3WBbWO2lMZSXgYcNall2xouqZlmtNdWEZEFhhXvQ2DLb/7hnzNo5MEzcXl9s4KmHtzlvngniL+WzDWpp1Z6bsF2bR4URkj6F9LjzQJifGuYzh/3Of02gu7rE6yRo4pH7zY2n/GTZGY9d9wjpH6vqlPd+EXbCOGDeoRnnNHhTVYn/AIMwWyLLLeHcbk5IclI/5T0uq124gXARS1vgTAOFtxvRtvGHEJIvKNyrDNtJMwLgqYe3MeslpADEEW563ENAnMOLCSHFh8I9BIRVhay2Ph2ErAYo3EPA1K4t1v4mq61PByGrAQr3EOB6eDEhZDigcA8JT06O4amHt7FPByGrAO6cHCIG3QaAENIfmHETQkjBoHATQkjBoFVCSI5g2wDiAoWbkJzAU+qJK7RKCMkJPKWeuMKMO+dw6rx64Cn1xBXnjFtESiIyJyJfyzIgcpvgOY7e1Nl/fiUZHnhKPXEljlXyBQAvZxUI6YZT59UFD6MgrjgJt4h8EMCDAL6cbTjED6fOqwueUk9ccfW4vwjgDwC8x/YEEXkUwKMAsHHjxt4jI5meEUnyCXe/EhciM24R+SyAn6jqhbDnqeoxVZ1Q1YkNGzakFuBqhlNnQogJl4x7B4DdIvIbANYC+DsiclxVP59taMTLvFhVQgjxE+voMhH5dQD/TlU/G/Y8Hl1GCCHx4NFlhBAyxMTagKOqfw7gzzOJhBBCiBPMuAkhpGBQuAkhpGBQuAkhpGBQuAkhpGBQuAkhpGBQuAkhpGBQuAkhpGBQuAkhpGBQuAkhpGBQuAkhpGDwzElCyFAxM1fHoZcu480bTQBAtVLGwd1bh6qrJoWbEDI0zMzVMfXcRTSXbnc9XWw0MfXViwAwNOJN4SaEFIqZubq1R/3RU1c7RNujuaw4euoqhZsQQvrNzFwdT7xwqX2Idn2xgSdeuITZV9/AmSsLxqP+PIbprFYKNyEkFUyZMJDuCU5HT11ti7ZHo7mEp89dQ9SRMMN0ViuFm5AeCZu69zuG+mIDJREsqaIWEUuacZsy4amvXgQEbevCy46B5F6zLWuOEu3yiAzVWa0UbkJ6wDZ1B/q3EBaMYUmjhTKNuP3CP7IyWPhpLnfLaaO51JPXfE+1EmqHmGBVCSGkA9vUvZ8LYaYYTLFECa0tbpsF4q/eCF4rjF685qldWzoGHAAQmDPuWrWCs9M7E79XnqFwE9IDNhHq50JY1Hu9vtiwZuVR17Jl5iM+CyQuvXjN/uoRbyB54L4NeP5CvUPMK+XSUFkjQSjchPSAberez4WwKPvg7ko5NCsPXsuPbUbhQnlEOjxuoFNQk3rsk+O1rudNfOi9A19n6CcUbkJ6wDR1zzLbM4mdKQY/Iu4zgGDcSWYOAkRWlUSV9aUh5sMMhZuQHjBN3bPK9mxid3jPGA7vGcNjJ+aNr1u80XRe1AvGHXcxUAzXM90LWyZ//Ny19s/9XOjNQ2VQHERjLCq4MjExobOzs6lfl5DVzI4jp40i6i3Chf3+gfs2ONU6/+jIgx0/BweLOFTKJRzeM9a1MBp3MMh6kdH0Gf2x9wsRuaCqEy7PZcZNSEGwiV19sdEW7WCFRaVcwqb3VZxEu1opdz0WnFGYqlFseFUqALpmCrZKEBNZL/TmoTIoLhRuQnKIaepeChFNT9QVt8vj4mTa5RHBwd1bjb/z2x2bp0/G+hz1xQYef/ZiV9xx5vlZL/TmoTIoLhRuQkIYhPdp87JdM10FsH60lT37PWMbUTss/dhsDtugIohX4x2kH2V9eagMikvkQQoislZEviMiF0Xksogc6kdghAwaT0Driw0obgvozFw90/e1Td2DC39hvHmj6eQj+/3jHUdOY/P0Sew4ctr6Gad2bUGlXOp4rFIu4ZH77+16PI4d4lEaEVQrZchKbP3wmW2fKc914C4Z97sAdqrqL0SkDODbIvK/VfVcxrERMlD64X2aMvqk/TiSUF9sYNuhb+Ltm7eceoqEVdEEa6njbk0HgPfcuQbzBz4N4Pa92XdiPtPZTj8rg9IiVlWJiIwC+DaAf6Wq523PY1UJGQY2T580iqUAeCVQfZEEWzXD2vJI+/QWFyrlUqKqjyh6reawVbmE4d1b10qPopXxhRGnqsTpzEkRKYnIPICfAPhWmGgTMizYPM60vE9bRq+Krql7GIf3jKFWrbTthTiWShhetUpSayiJ1eDd27DZjsegrKw84CTcqrqkqtsAfBDAJ0Tko8HniMijIjIrIrMLCwtpx0lI38na+7RZIm81ms5iXBLB5HgNZ6d34pUjD+Ls9M5ULZVexHByvNZeJHXBf29dKj1cxH1YiVVVoqqLInIGwGcAfD/wu2MAjgEtqyS1CAnJGNt0Oyvv03s/25ekOlru2nG4f+aSsULkkfvv7XqsltBfthHl64fZFQce2uq0gackgs99vNb2tG314v7ZTi9lfEW3WCKFW0Q2AGiuiHYFwD8G8J8yj4yQPhDVlzrtHhguOxFNy05PTo4BAJ45fx1LqiiJ4JH7720/7mdq1xbsOzEfmnmPCGBol22lvtJhMG5fb//gZxtMyiXBw79yb0eHP5NoB2c7Scv48tBDvVdcrJIPADgjIn8J4LtoedxfyzYsQvqDbbp96KXLfXu/IG81uhcmZ+bqOHNloS3aS6o4c2XBaGFMjtewd/vG0PdIMiU2WSYudoVn5dQsgrrujjU4c2XBeF9KItbSQFcra2au3lHqeOily4W3WCIzblX9SwDjfYiFkL5jm1a/eaNpzDBN+Kfd1dEyVFvia5qCu0zjgxljkhNuvEzctgEnyZ6YRnMJv//sfLuZVbVSxqJhkAHMnzPM0zcNVgCwrGqt4HGxskzZtY0875QMwp2TZFUTVm/sUq8dFAZ/GZ937uKhly63O/TdHSJ2gDljdD3hJsiTk2P42sUfG98vbPt8GH57JexzmOyKKGsjie0RZWW59iF3ea884VRVQsiwElYh4pKBRQlDc1nx5o1mu1zt7Zu3WgcMWFhb7v5KupxwY+Pg7q3WnY5plQ0GCQ4+nlXhNZcyPbeXCp6gFeK3c1yz6LzvlAzCjJsMPWEVBJPjNRx88bIxe3TJwOJOr5tLivWjZYzesQavLzZwd6XcsWvxzRvNLvsjahdiWJxRdoJLAyoXSiJYVm0fJeZVhwQ/X7AJVtDaiFPpMTNXx6GXLnfNcvz3z3bvqpUy1t25prBVJezHTXJLGiVbLjvweunH3MvuwLDX+3cthlWi2OJ0vXfe89IoHxSgS6ht9LorM6o6x7t+Xnptu5D6zklC+k1au+Jcqx6CG15cv9imKX4UcWuR/fEBrewWIXHGuXdexUcYIc5OB4qW7+1yiHCvC4FRFpV3/V7+tnmGVgnJJWk1eHLdpJG0XjtoRfirSkzZZ9Ja5LD4gtn12+/eSrU5Vpx6b1d6XQiMEn7/9YfxPEoKN8klaTW370ev5TiiGrQsej1sOK1yN5FkJYJJSGMhMMz3L9pCYxIo3CSXpCW4/T6FPUhUttfrtvq0yt323r/R6dCFJJRHBHetXdMuiUxjIdB2sn21UsbB3VuHLsMOQuEmuSQtwS1Cr+VepvKuMxBBeOnjk5NjeGXhFzj71284X69cEtyM8LOzEtIi/F2zhMJNckmaX8xh9Dg9XA8sUET34Xj6X34SM3N14xmRQGfJ39SuLTj44mXcDNmEAwDv3lqOjC0pw/x3jYLCTXLLav5iumKzDILY+oQE8e63SwndvpWt72Hk/bT0osJyQEIKRHCXINB5kEK1Uka51Fm/F9dici2hc11vKFIPkKLADTiEFIS8Hefl0qIW6H2zzWohzgYcCjchBcFll2W/8Q8Strr1w3tanQqHeSExjcEyjnDT4yakIKRV254mwXUIk4ABKPzBBWEM4mAGCjchBaEfm4l6xbSgvOPI6VR3cuaNtHb5xoGLk4QUhKwPL86KPM4U0mQQn4/CTUhBKGrDJNuMIE8zhV4YxOejcBNSICbHa5jatQX3VCt4fbGBo6euxu6Y2G+KOlNwZRCfjx43IQUiDyeUx62gGPbt6YP4fCwHJCRHRInioEsCi3QwQdHgQQqEFBCXAxAGvdDncjAFyR4KNyE5wUUUB73QN+iBg7SgcBOSE1xEcdALfYMeOEgLCjchOcFFFAddEjjogYO0YFUJITnB9fCIQba7HfYKkaJA4SYkJxRFFNknffBECreI3AvgzwD8EloHaRxT1S9lHRghqxGKInHBJeO+BeBxVf2eiLwHwAUR+Zaq/iDj2AghhBiIXJxU1R+r6vdW/v1zAC8DYEpACCEDIlZViYhsAjAO4Lzhd4+KyKyIzC4sLKQTHSGEkC6chVtE7gLwPIDHVPVnwd+r6jFVnVDViQ0bNqQZIyGEEB9Owi0iZbRE+2lVfSHbkAghhIQRKdwiIgC+AuBlVf2j7EMihBAShkvGvQPA7wDYKSLzK//7jYzjIoQQYiGyHFBVvw1A+hALIYQQB7hzkgycuI35CVntULjJQMnDiS6EFA12ByQDhY35CYkPhZsMFDbmJyQ+FG4yUNiYn5D4ULjJQEnamH9mro4dR05j8/RJ7DhyuuNcRkKGHS5OkoGSpAc1FzTJaofCTTInqtwvbg/qsAVNCjdZDVC4SaZkkR1zQZOsduhxk0zJotyPC5pktUPhJpmSRXYcZ0GTi5hkGKFVQhLhuk39nmoFdYNI95Id2xY0AWDHkdPtxx64bwOev1DnIiYZOkRVU7/oxMSEzs7Opn5dkj5J+oQEfWuglfEe3jPW9VrTc8sjgrvWrsHijWZqvUlM7yNonW4dpFat4Oz0zp7ej5C0EZELqjrh8lxaJasYT+zqiw0obmekUXZCHN96cryGw3vGUKtWIACqlTIgwJs3mu333HdiHpt6tDJMMdlSEi5ikqJD4c4R/fZjky4cxvGtgxm9CNBc6pRU7yfXgSNOTCa4iEmKDj3unNBL2VzStqhJFw5dfWvTZ4oiaT22LaagXeKyK5OQvMOMOyckzX5d7A5bJp+0rM61qsP0mVxIYmXYYtq7fWPbpqlVK0YfnpCiQeHOCUmz3yjBDxP2pH1Cgr61TRCTeskKYP/MJevvTQORKabPfbyGM1cWeEADGTpoleSEpGVzUYIfJuxeZcWhly7jzRtNAMCda9zGcpdt6rbP5MLxc9cAAE9OjnU8HmUpeTG5Wk88fYcUEWbcOSFp9htld7hk8u80l9v/Xmw08cQLl7B/5lLPC6WmzxSHZ85f73rMNhA9/uzFjhhdrKekVTWEDBoKd04wlc2tLY9g34n5UOF84L4NoY9HCbtN4J4+d61nQfN/piQsGfYY2AaiJdWOGF0GLNtnP/jiZe62JLmGwp2ArMr2JsdrODu9E089vA3v3lruqHW2CeeZKwvGaz1z/jo2T5/EjZu3UB6Rjt/5M3mbwAUlM2l/kcnxGqZ2bYFEP9WI64JqMEbb80ZE2te02TiLjSazcJJrKNwx6cf0Ok6FSVgGqmhtdGku35bhaqXcsZAYp6Y56WLj0VNXrZthogTdu8ePnZjHtkPfxAP3bQi1X7wYbTMR777UFxvOgwnPwCR5g8Idk6wOt/Wy+E3TJ62ZoEk4424meffWcsfPU7u2oFxykzDvveLOOMIEP07DhcVGE8fPXQstMfRitM1Egu/tKt5JF1kJyQIKd0zS6HYXFL79M5faWXwYJpGOuwBoHGQC6jkCdIm5Z68kmXHEGVw8jz8JAkRaQEHU9561agXrR8vWa9MuIXmBwh2TXntBm4Tv6YgsErBXmAQXNUsSLXvBBTq/lQIAywDW3bHGWKedZMZhsy1M1FfK8pKgQGwLyGs49cqRB3F2eicOPLTVOHAoQLuE5IbIOm4R+RMAnwXwE1X9aPYh5ZupXVuMnfFct1HHaYbkx+9Lm2qPvZrsmbk69p2YD72mX9RsmelbjSbmD3y663GXGcf+mUv4H+evYTmOD+LDW1ANDihR+KtXTH+nIKa/2+R4DY+dmDc+v77YaG/2IWSQuGzA+e8A/guAP8s2lGKQ5HBbP0kW+GrVivPGksnxGmZffQNPn7tmFO+gWNk2ydxdKbd7W1dHy1BtifmIiLFMb0QEM3N1zL76RnvzTFLevNFEuSQYLY/gRnM5+gXo/ly2++D1LqmF/N1qIRuH2M+b5AGnftwisgnA11wzbvbjtmMrQ7P1jg72uba9Pthjemau3rEjEgDWj5Zx4KGtXTsHTf2ylwEsxcx4K+US3rm1hLRavNdWDkOwDUJRIux6r4KY7kmc1xOShDj9uLnlvc/YrBavr0Z9sYHSSlZrEqQ4i6PvBLLV4M+AeQaxeOMm3r4ZvzlUkoZSYby+2MCTk2OY+NB7cfTU1ch7Y3p9nMc9vGvaLBP28yaDJjXhFpFHATwKABs3bkzrskNHr1aLa0+TsEXE4HsF+45smj7pFEvWeJ/JpS+K7fVx+7/41w9KFluI/bzJoElNuFX1GIBjQMsqSeu6w0hSIQLcF0ezOKTXj03U7igJbi6Z//zVShnK8fOWAAAI10lEQVSLjabxd0HS6Jsddq9MC7wAOp5v+nzs503yAK2SguGascfNNv1CJoJIn3r731uP7117q0sU71wzgpsGca5Wyji4e6vRO14/WsaD/+ADoS1Yk3TxCztU2LTAu7Y8YrR7SiJYVmX3QJIbXMoBnwHw6wDeLyKvATigql/JOjBixyVjj1O22LUY5zBf+tHfNnB4z1iXKO6z+MJvNZqJbaJeTgfyqkueOX8d9cUGHn/2Iu5YI2gE/P5Gc8nq0S+r4pUjD4a+DyH9JFK4VfWRfgRC0sVUDjdi2ZtjO6kmLPN+fbHRNYDMzNWt5YK9+NVx/HovDm9waGXRt0V6SRWNZjwnj542yRu0SlIkT035Z+bqOPGd6x3J89s3lzD13EUAcKpUUW3ZGP6SQo+gmO2fueRcOx6XuIcT+7PzYGYdRrVSxru3lhNvriKkX3DLe0rkrSm/aSs70DphPbh1OyyjVEXkAQ8zc3WraJdEej7nsWrpH2KKO+k5l5VyCQd3b3U6ko2QQcOMOyXiTuezJqx6JPi7qV1brDXLbzWaeOrhbaEzibC2rcuqkXZG2OxkZq6OX7xzq+vxckmMmbBr1cyIAB+4u2J8fwo1yTsU7pTIuvwurg0Tdt5jMFOdHK/h4IuXjaV696xst0+y0SX4XvtnLuGZ89e7PPCwxUbbzGHdHWuMMbmec/nb92/sOs+SkKJAqyQleu0aGEYSG2Zq15auk2+AVqb6wH0buvppH9y9NdGZl4D9M/rbrO6fuYTj564ZFy6B+AdFvGWpBze1uR3B7YXZkgg+v52iTYoNM+6U6LVrYBhJbBjvcX8m7dVLP3+h3lVad3jPmLG8z8U2MH12AfCrH25tVY/qVuhhOygiTj163JLDLBaU87RITYYTCndK9LqVPYxeem6YGi/ZBoGz0zsTxWv67A/ct6FjgHDBdlBE3AHRteSwl/rwfl6TkCAU7hTpZSt7GEl6btjIyosPfnbTABFG2EERQDYDYhYLynlbpCbDCYW7AKRpw6Q5CIQRZyCI6vSX9oDoWRlxzvZ0tT+yXqQmBKBwF4I0s84svXg/UdUdJRE8cv+9fV8kjOq1DXQPYnHsj34NjGR1Q+EuCGllnWkMAi7Zp22AGPSGlqgNOqZBLI790a+BkaxuKNxDhouo9jIIuGafWXrTwXjivEeUZXHnmu4K2Tj2R78+N1ndULiHiH5UNPRyQENcokQ5yeeNsnAWG82uayQpSaRQkyzhBpwhwiaqjz97sWOzTS/0a/HNZdNR2CBiw7RBJ0jwGqbX0P4gg4QZ9xBhE09vt2IaGXi/Ft9cMvskg0jQyrBtDPJfY9D2Bzf0kCAU7iHCpU9HLzXFM3N13LjZ3fApi+zTRZSTDiJ+K8N2Erypn8sgxJIbeogJWiVDhIsNACSzNTwBCfbmrlbKPVWKzMzVu/qmAG69X9KwMPJugySxg8jww4x7iAhO6aNOo4mDrYxu3Z3mLn0uhGWTLmV1aVgYg7ZBouCGHmKCwj1k+Kf0ps0mSbPJMAFJ6sGGZZNnp3e2n5NVaWOa18gKbughJijcCSjKYlGa2aRNQKqj5cQebFQ2mWdB7Rfc0ENMULhjUrTForTEzyYgqkjcVCkv2WSeB+K8WzlkMFC4Y7Jau7/ZBGSf5cgzFw82D9lkEQZizjxIEAp3TFbzYpFJQGxd9lyy5jxkk6t1ICbFhsIdk7xM7/NCr1nzoLPJ1TwQk+LCOu6Y5L3ut99MjtdweM8YatUKBK3e2oPuABiHLM8KJSQrmHHHJA/T+7wx6Ky5F/LgsxMSFwp3AoosVKQTDsSkiDgJt4h8BsCXAJQAfFlVj2QaFSF9hAMxKRqRHreIlAD8VwD/BMBHADwiIh/JOjBCCCFmXBYnPwHgr1T1h6p6E8D/BPBPsw2LEEKIDRfhrgG47vv5tZXHOhCRR0VkVkRmFxYW0oqPEEJIgNTKAVX1mKpOqOrEhg0b0rosIYSQAC7CXQdwr+/nD648RgghZACIGvo1dzxBZA2A/wfgU2gJ9ncB/LaqXg55zQKAV1OMM8j7Afw0w+sXHd6fcHh/wuH9CSer+/MhVXWyKyLLAVX1loj8GwCn0CoH/JMw0V55TaZeiYjMqupElu9RZHh/wuH9CYf3J5w83B+nOm5V/TqAr2ccCyGEEAfYq4QQQgpGUYX72KADyDm8P+Hw/oTD+xPOwO9P5OIkIYSQfFHUjJsQQlYthRJuEfmMiFwVkb8SkelBx5MnROReETkjIj8Qkcsi8oVBx5RHRKQkInMi8rVBx5I3RKQqIs+JyBUReVlEPjnomPKEiOxb+W59X0SeEZG1g4qlMMLNZleR3ALwuKp+BMB2AP+a98fIFwC8POggcsqXAHxDVe8D8DHwPrURkRqAfwtgQlU/ilZp9D8fVDyFEW6w2VUoqvpjVf3eyr9/jtaXjr1KfYjIBwE8CODLg44lb4jI3QB+DcBXAEBVb6rq4mCjyh1rAFRWNiWOAnh9UIEUSbidml0RQEQ2ARgHcH6wkeSOLwL4AwDLgw4kh2wGsADgT1espC+LyLpBB5UXVLUO4D8DuAbgxwDeUtVvDiqeIgk3cUBE7gLwPIDHVPVng44nL4jIZwH8RFUvDDqWnLIGwC8D+GNVHQfwNgCuI60gIuvRmuFvBnAPgHUi8vlBxVMk4WazqwhEpIyWaD+tqi8MOp6csQPAbhH5EVo2204ROT7YkHLFawBeU1VvlvYcWkJOWvwjAK+o6oKqNgG8AOBXBxVMkYT7uwD+vohsFpE70FoYeHHAMeUGERG0/MmXVfWPBh1P3lDVJ1T1g6q6Ca3/dk6r6sAypryhqn8D4LqIeKckfwrADwYYUt64BmC7iIyufNc+hQEu3hbmsOAkza5WGTsA/A6ASyIyv/LYv1/pM0OIC78H4OmVxOiHAH53wPHkBlU9LyLPAfgeWhVccxjgDkrunCSEkIJRJKuEEEIIKNyEEFI4KNyEEFIwKNyEEFIwKNyEEFIwKNyEEFIwKNyEEFIwKNyEEFIw/j/h7eCdkxWSXAAAAABJRU5ErkJggg==\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"data = sio.loadmat(\\\"ex7data2.mat\\\")\\n\",\n    \"X = data[\\\"X\\\"]\\n\",\n    \"plt.plot(X[:, 0], X[:, 1], 'o')\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Implementing _K_-Means\\n\",\n    \"\\n\",\n    \"The algorithm consists of two parts:\\n\",\n    \"1. Assign each data point to the closest centroid. $idx_i$ corresponds to $c^{(i)}$, the index of the centroid assigned to example $i$.\\n\",\n    \"2. Compute means based on centroids assignments.\\n\",\n    \"\\n\",\n    \"One runs the algorithm for a certain number of iterations. The algorithm will always converge, but not necessarily to the optimal value. Therefore, one should run the algorithm multiple times with different random initalizations and choose the one with the lowest cost function value (distortion). \\n\",\n    \"\\n\",\n    \"**Exercise**: Start by initializing _K_ random centroids for the data.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 3,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def initialize_K_centroids(X, K):\\n\",\n    \"    return None\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"The following should return three points from the dataset.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 4,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"initialize_K_centroids(X, 3)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"**Exercise**: Implement part 1 of the _K_-means algorithm (cluster assignment step)\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 5,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def find_closest_centroids(X, centroids):\\n\",\n    \"    m = len(X)\\n\",\n    \"    c = np.zeros(m)\\n\",\n    \"    return c\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 6,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"K = 3\\n\",\n    \"initial_centroids = np.array([[3, 3], [6, 2], [8, 5]])\\n\",\n    \"idx = find_closest_centroids(X, initial_centroids)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"**Exercise**: Implement part 2 of the _K_-means algorithm (Move centroid step). Make sure it is vectorized.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 7,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def compute_means(X, idx, K):\\n\",\n    \"    m, n = X.shape\\n\",\n    \"    centroids = np.zeros((K, n))\\n\",\n    \"    return centroids\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"The following code should return approximately:\\n\",\n    \"$$\\n\",\n    \"\\\\begin{bmatrix}\\n\",\n    \"2.428 && 3.158 \\\\\\\\\\n\",\n    \"5.814 && 2.634 \\\\\\\\\\n\",\n    \"7.119 && 3.617 \\n\",\n    \"\\\\end{bmatrix}\\n\",\n    \"$$\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 8,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"array([[0., 0.],\\n\",\n       \"       [0., 0.],\\n\",\n       \"       [0., 0.]])\"\n      ]\n     },\n     \"execution_count\": 8,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"centroids = compute_means(X, idx, K)\\n\",\n    \"centroids\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Running _K_-means\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 9,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def find_k_means(X, K, max_iters=10, plot=False):\\n\",\n    \"    _, n = X.shape\\n\",\n    \"    centroids = initialize_K_centroids(X, K)\\n\",\n    \"    centroid_history = np.zeros((max_iters, K, n))\\n\",\n    \"    for i in range(max_iters):\\n\",\n    \"        idx = find_closest_centroids(X, centroids)\\n\",\n    \"        centroids = compute_means(X, idx, K)\\n\",\n    \"\\n\",\n    \"        if plot:\\n\",\n    \"            centroid_history[i] = centroids\\n\",\n    \"     \\n\",\n    \"    if plot:\\n\",\n    \"        for centroid in range(K):\\n\",\n    \"            # Plot examples for this centroid\\n\",\n    \"            examples = X[np.where(idx == centroid)]\\n\",\n    \"            plt.plot(examples[:, 0], examples[:, 1], 'o')\\n\",\n    \"            \\n\",\n    \"            # Plot centroid history\\n\",\n    \"            history = centroid_history[:, centroid, :]\\n\",\n    \"            plt.plot(history[:, 0], history[:, 1], '-xk')\\n\",\n    \"    \\n\",\n    \"    return centroids, idx\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 10,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"centroids, idx = find_k_means(X, K, plot=True)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Image compression with _K_-means\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 11,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<PIL.PngImagePlugin.PngImageFile image mode=RGB size=128x128 at 0x1299BBEF0>\"\n      ]\n     },\n     \"execution_count\": 11,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"from PIL import Image\\n\",\n    \"image = Image.open('bird_small.png')\\n\",\n    \"X = np.asarray(image) / 255 # range 0 - 1\\n\",\n    \"\\n\",\n    \"width, height, depth = X.shape\\n\",\n    \"X = X.reshape((width * height, depth))\\n\",\n    \"\\n\",\n    \"image\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"**Exercise**: Try out different values for *K* and `max_iters`.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 12,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"image/png\": \"iVBORw0KGgoAAAANSUhEUgAAAIAAAACACAIAAABMXPacAAAARElEQVR4nO3BAQEAAACAkP6v7ggKAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAYwIAAAWMWdQAAAAAASUVORK5CYII=\\n\",\n      \"text/plain\": [\n       \"<PIL.Image.Image image mode=RGB size=128x128 at 0x1299BB160>\"\n      ]\n     },\n     \"execution_count\": 12,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"# Run K-means\\n\",\n    \"K = 15\\n\",\n    \"colors, id2 = find_k_means(X, K, max_iters=10)\\n\",\n    \"idx = find_closest_centroids(X, colors)\\n\",\n    \"\\n\",\n    \"# Reconstruct image\\n\",\n    \"idx = np.array(idx, dtype=np.uint8)\\n\",\n    \"X_reconstructed = np.array(colors[idx, :] * 255, dtype=np.uint8).reshape((width, height, depth))\\n\",\n    \"compressed_image = Image.fromarray(X_reconstructed)\\n\",\n    \"compressed_image\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Principal Content Analysis\\n\",\n    \"---\\n\",\n    \"In this exercise, you will use principal component analysis (PCA) to perform dimensionality reduction. You will first experiment with an example 2D dataset to get intuition on how PCA works, and then use it on a bigger dataset of 5000 face image dataset.\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Dimension reduction on example dataset\\n\",\n    \"\\n\",\n    \"Before using PCA it's important to use feature scaling to make sure every feature 'is of equal importance' when runnig PCA.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 13,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"[<matplotlib.lines.Line2D at 0x129ae0b70>]\"\n      ]\n     },\n     \"execution_count\": 13,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"data = sio.loadmat(\\\"ex7data1.mat\\\")\\n\",\n    \"X = data[\\\"X\\\"]\\n\",\n    \"plt.plot(X[:, 0], X[:, 1], 'o')\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 14,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def normalize_features(X):\\n\",\n    \"    mu = np.mean(X, axis=0)\\n\",\n    \"    sigma = np.std(X, axis=0)\\n\",\n    \"    return (X-mu)/sigma, mu, sigma\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 15,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"X_norm, mu, sigma = normalize_features(X)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"PCA consists of two steps: first you compute the covariance matrix of the data given by:\\n\",\n    \"$$ \\\\Sigma = \\\\frac{1}{m}X^TX$$\\n\",\n    \"\\n\",\n    \". Second you compute the [eigenvectors](https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors) of this matrix using numpy: `U, S, V = np.linalg.svd(Sigma)`.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 16,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def pca(X):\\n\",\n    \"    m = len(X)\\n\",\n    \"    Sigma = (1/m) * X.T @ X\\n\",\n    \"    U, S, _ = np.linalg.svd(Sigma)\\n\",\n    \"    return U, S\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"The following code should return approximately $\\\\begin{bmatrix} -0.707 && -0.707\\\\end{bmatrix}$.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 17,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"(-0.7071067811865474, -0.7071067811865474)\"\n      ]\n     },\n     \"execution_count\": 17,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"U, S = pca(X_norm)\\n\",\n    \"U[0, 0], U[1, 0]\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 18,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def project_data(X, U, K):\\n\",\n    \"    Ureduce = U[:, :K]\\n\",\n    \"    z = X @ Ureduce\\n\",\n    \"    return z\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"The following should return approximately $1.496$.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 19,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"array([1.49631261])\"\n      ]\n     },\n     \"execution_count\": 19,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"Z = project_data(X_norm, U, K=1)\\n\",\n    \"Z[0]\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"**Exercise**: Implement `recover_data`.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 20,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def recover_data(Z, U, K):\\n\",\n    \"    return None\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 21,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"ename\": \"TypeError\",\n     \"evalue\": \"'NoneType' object is not subscriptable\",\n     \"output_type\": \"error\",\n     \"traceback\": [\n      \"\\u001b[0;31m---------------------------------------------------------------------------\\u001b[0m\",\n      \"\\u001b[0;31mTypeError\\u001b[0m                                 Traceback (most recent call last)\",\n      \"\\u001b[0;32m<ipython-input-21-14b452ab9da0>\\u001b[0m in \\u001b[0;36m<module>\\u001b[0;34m\\u001b[0m\\n\\u001b[1;32m      1\\u001b[0m \\u001b[0mX_rec\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mrecover_data\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mZ\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mU\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mK\\u001b[0m\\u001b[0;34m=\\u001b[0m\\u001b[0;36m1\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m----> 2\\u001b[0;31m \\u001b[0mplt\\u001b[0m\\u001b[0;34m.\\u001b[0m\\u001b[0mplot\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mX_rec\\u001b[0m\\u001b[0;34m[\\u001b[0m\\u001b[0;36m0\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;34m:\\u001b[0m\\u001b[0;34m]\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mX_rec\\u001b[0m\\u001b[0;34m[\\u001b[0m\\u001b[0;36m1\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;34m:\\u001b[0m\\u001b[0;34m]\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;34m'o'\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\\u001b[1;32m      3\\u001b[0m \\u001b[0mplt\\u001b[0m\\u001b[0;34m.\\u001b[0m\\u001b[0mtitle\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;34m\\\"Recoverd data\\\"\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;31mTypeError\\u001b[0m: 'NoneType' object is not subscriptable\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"X_rec = recover_data(Z, U, K=1)\\n\",\n    \"plt.plot(X_rec[0, :], X_rec[1, :], 'o')\\n\",\n    \"plt.title(\\\"Recoverd data\\\")\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### PCA on faces\\n\",\n    \"In this part of the exercise, you will run PCA on face images to see how it can be used in practice for dimension reduction.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": null,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"data = sio.loadmat(\\\"ex7faces.mat\\\")\\n\",\n    \"X = data[\\\"X\\\"]\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": null,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def display_samples(X):\\n\",\n    \"    rows = 4\\n\",\n    \"    size = int(np.sqrt(len(X.T)))\\n\",\n    \"    num_samples = rows ** 2\\n\",\n    \"    samples = X[:num_samples]\\n\",\n    \"    display_img = Image.new('RGB', (rows*32, rows*32))\\n\",\n    \"\\n\",\n    \"    # loop over the images, turn them into a PIL image\\n\",\n    \"    i = 0\\n\",\n    \"    for col in range(rows):\\n\",\n    \"        for row in range(rows):\\n\",\n    \"            array = samples[i]\\n\",\n    \"            array = ((array / max(array)) * 255).reshape((size, size)).transpose() # redistribute values\\n\",\n    \"            img = Image.fromarray(array + 128)\\n\",\n    \"            display_img.paste(img, (col*32, row*32))\\n\",\n    \"            i += 1\\n\",\n    \"\\n\",\n    \"    # present display_img\\n\",\n    \"    plt.imshow(display_img, interpolation='nearest')\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": null,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"display_samples(X)\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": null,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"K = 100\\n\",\n    \"X_norm, mu, sigma = normalize_features(X)\\n\",\n    \"U, S = pca(X_norm)\\n\",\n    \"Z = project_data(X_norm, U, K)\\n\",\n    \"X_rec = recover_data(Z, U, K)\\n\",\n    \"display_samples(X_rec.T)\"\n   ]\n  }\n ],\n \"metadata\": {\n  \"kernelspec\": {\n   \"display_name\": \"Python 3\",\n   \"language\": \"python\",\n   \"name\": \"python3\"\n  },\n  \"language_info\": {\n   \"codemirror_mode\": {\n    \"name\": \"ipython\",\n    \"version\": 3\n   },\n   \"file_extension\": \".py\",\n   \"mimetype\": \"text/x-python\",\n   \"name\": \"python\",\n   \"nbconvert_exporter\": \"python\",\n   \"pygments_lexer\": \"ipython3\",\n   \"version\": \"3.7.1\"\n  }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n"
  },
  {
    "path": "ex8/Anomaly Detection and Recommender Systems (Exercises).ipynb",
    "content": "{\n \"cells\": [\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"# Anomaly Detection and Recommender Systems\\n\",\n    \"\\n\",\n    \"Stanford CS229 - Machine Learning by Andrew Ng. Programming exercise 8.\\n\",\n    \"\\n\",\n    \"Please check out [the repository on GitHub](https://github.com/rickwierenga/CS229-Python/). If you spot any mistakes or inconcistencies, please create an issue. For questions you can find me on Twitter: [@rickwierenga](https://twitter.com/rickwierenga). Starring the project on GitHub means a ton to me!\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 1,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"import numpy as np\\n\",\n    \"import matplotlib.pylab as plt\\n\",\n    \"import scipy.io as sio\\n\",\n    \"from scipy.optimize import minimize\\n\",\n    \"%matplotlib inline\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Anomaly detection\\n\",\n    \"\\n\",\n    \"$x \\\\in \\\\mathbb(R)$ is a distributed Gaussian with mean $\\\\mu$ and variance $\\\\sigma$.\\n\",\n    \"\\n\",\n    \"$x \\\\sim \\\\mathcal{N}(\\\\mu, \\\\sigma^2)$ ($\\\\sim$: distributed as)\\n\",\n    \"\\n\",\n    \"We fit the parameters\\n\",\n    \"\\n\",\n    \"$\\\\mu = \\\\frac{1}{m}\\\\displaystyle\\\\sum_{i = 1}^{m}x^{(i)}$, $\\\\sigma = \\\\frac{1}{m}\\\\displaystyle\\\\sum_{i = 1}^m(x^{(i)} - \\\\mu)$.\\n\",\n    \"\\n\",\n    \"Then we use the following function:\\n\",\n    \"\\n\",\n    \"$$p(x;\\\\mu, \\\\sigma^2) = \\\\displaystyle\\\\prod_{j = 1}^{n}p(x_j; \\\\mu_j, \\\\sigma^2)$$\\n\",\n    \"\\n\",\n    \"Anomaly if $p(x) < \\\\epsilon$.\\n\",\n    \"\\n\",\n    \"### Algorithm\\n\",\n    \"1. Choose features $x_j$.\\n\",\n    \"2. Fit parameters $\\\\mu_1, ..., \\\\sigma_n$, $\\\\mu_1, ..., \\\\sigma_n$.\\n\",\n    \"3. Given new example $x$, compute $p(x)$.\\n\",\n    \"\\n\",\n    \"### Anomaly Detection vs Supervised Learning\\n\",\n    \"Use *anomaly detection*:\\n\",\n    \"* Very small number of positive examples ($y = 1$).\\n\",\n    \"* Many different \\\"types\\\" of anomaly.\\n\",\n    \"* Future anomalies may look nothing like any of the anomalous examples we've seen so far.\\n\",\n    \"\\n\",\n    \"Use *supervised learning*:\\n\",\n    \"* Large number of positive and negative examples.\\n\",\n    \"* Enough positive examples for the algorithm to get a sense of what positive examples look like.\\n\",\n    \"* Future examples look like examples from the dataset.\\n\",\n    \"\\n\",\n    \"### Tips\\n\",\n    \"* Examine the examples the model got wrong by hand and try to come up with new features. \\n\",\n    \"* Have a look at the distribution. If it doesn't look like a bell curve, apply log or square root function to each traning example.\\n\",\n    \"\\n\",\n    \"### Multivariate Gaussian Distribution\\n\",\n    \"![mgd](images/mgd.png)\\n\",\n    \"\\n\",\n    \"Instead of modelling $p(x_1), p(x_2), ...$ seperately, we model $p(x)$ in one go. Parameters $\\\\mu \\\\in \\\\mathbb{R}^n$, $\\\\Sigma \\\\in \\\\mathbb{R}^{n \\\\times n}.$\\n\",\n    \"\\n\",\n    \"#### Original vs Multivariate\\n\",\n    \"With the original model you have to manually create featuers to capture anomalies where $x_1$, $x_2$ take unusual combinations of values where the multivariate model automatically captures the correlations. The original model is computationaly cheaper and works OK when $m$ is small (the multivariate model must have $m > n$.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 2,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"image/png\": \"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\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"data = sio.loadmat('ex8data1.mat')\\n\",\n    \"X = data[\\\"X\\\"]\\n\",\n    \"plt.plot(X[:, 0], X[:, 1], 'bx')\\n\",\n    \"plt.xlabel('Latency (ms)')\\n\",\n    \"plt.ylabel('Throughput (mb/s)')\\n\",\n    \"plt.show()\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"**Exercise**: Complete the `estimate_gaussian` function to return an n-dimensional vector $\\\\mu$ that holds the mean for every feature and a vector $\\\\sigma^2$ that holds the variance.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 1,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def estimate_gaussian(X):\\n\",\n    \"    return 0, 0\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 2,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"ename\": \"NameError\",\n     \"evalue\": \"name 'X' is not defined\",\n     \"output_type\": \"error\",\n     \"traceback\": [\n      \"\\u001b[0;31m---------------------------------------------------------------------------\\u001b[0m\",\n      \"\\u001b[0;31mNameError\\u001b[0m                                 Traceback (most recent call last)\",\n      \"\\u001b[0;32m<ipython-input-2-1f80e79b7643>\\u001b[0m in \\u001b[0;36m<module>\\u001b[0;34m\\u001b[0m\\n\\u001b[1;32m      1\\u001b[0m \\u001b[0;32mfrom\\u001b[0m \\u001b[0mscipy\\u001b[0m\\u001b[0;34m.\\u001b[0m\\u001b[0mstats\\u001b[0m \\u001b[0;32mimport\\u001b[0m \\u001b[0mmultivariate_normal\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0;32m----> 2\\u001b[0;31m \\u001b[0mmu\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0msigma2\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mestimate_gaussian\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mX\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[0m\\u001b[1;32m      3\\u001b[0m \\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m      4\\u001b[0m \\u001b[0;31m# Create the grid for plotting\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\\u001b[1;32m      5\\u001b[0m \\u001b[0mX1\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mX2\\u001b[0m \\u001b[0;34m=\\u001b[0m \\u001b[0mnp\\u001b[0m\\u001b[0;34m.\\u001b[0m\\u001b[0mmeshgrid\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0mnp\\u001b[0m\\u001b[0;34m.\\u001b[0m\\u001b[0marange\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;36m0\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;36m35\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;36m0.5\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0mnp\\u001b[0m\\u001b[0;34m.\\u001b[0m\\u001b[0marange\\u001b[0m\\u001b[0;34m(\\u001b[0m\\u001b[0;36m0\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;36m35\\u001b[0m\\u001b[0;34m,\\u001b[0m \\u001b[0;36m0.5\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m)\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0;34m\\u001b[0m\\u001b[0m\\n\",\n      \"\\u001b[0;31mNameError\\u001b[0m: name 'X' is not defined\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"from scipy.stats import multivariate_normal\\n\",\n    \"mu, sigma2 = estimate_gaussian(X)\\n\",\n    \"\\n\",\n    \"# Create the grid for plotting\\n\",\n    \"X1, X2 = np.meshgrid(np.arange(0, 35, 0.5), np.arange(0, 35, 0.5))\\n\",\n    \"grid = np.vstack((X2.flatten(), X1.flatten())).T\\n\",\n    \"\\n\",\n    \"Z = multivariate_normal.pdf(x=grid, mean=mu, cov=sigma2)\\n\",\n    \"Z = Z.reshape(X1.shape)\\n\",\n    \"\\n\",\n    \"plt.contour(X1, X2, Z, np.array([10.]) ** np.arange(-21, 0, 3.))\\n\",\n    \"plt.plot(X[:, 0], X[:, 1], 'bx')\\n\",\n    \"plt.xlabel('Latency (ms)')\\n\",\n    \"plt.ylabel('Throughput (mb/s)')\\n\",\n    \"plt.show()\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### The $F_1$ score and choosing $\\\\epsilon$\\n\",\n    \"Remember:\\n\",\n    \"$$prec = \\\\frac{tp}{tp + fp}$$\\n\",\n    \"$$rec = \\\\frac{tp}{tp+fn}$$\\n\",\n    \"\\n\",\n    \"* $tp$ is true positive\\n\",\n    \"* $tp$ is false positive\\n\",\n    \"* $tp$ is false negative\\n\",\n    \"* $precision$ is precision\\n\",\n    \"* $recall$ is false negative\\n\",\n    \"\\n\",\n    \"$$F_1 = \\\\frac{2 * prec * rec}{prec + rec}$$\\n\",\n    \"\\n\",\n    \"For this dataset we use the $F_1$ score to measure the accuracy because there are very few negative traning examples.\\n\",\n    \"\\n\",\n    \"**Exercise**: Write a method the compute the $F_1$ score and select the best $\\\\epsilon$.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 4,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def select_threshold(ycv, pcv):\\n\",\n    \"    return 1, 1\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"You should find the best $F_1$ score for $\\\\epsilon \\\\approx 8.99\\\\cdot10^{-05}$ and $F_1 = 0.875$. \"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 6,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stderr\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/ipykernel_launcher.py:15: RuntimeWarning: invalid value encountered in long_scalars\\n\",\n      \"  from ipykernel import kernelapp as app\\n\"\n     ]\n    },\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"(8.990852779269493e-05, 0.8750000000000001)\"\n      ]\n     },\n     \"execution_count\": 6,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"Xcv = data[\\\"Xval\\\"]\\n\",\n    \"ycv = data[\\\"yval\\\"].flatten()\\n\",\n    \"pcv = multivariate_normal.pdf(x=Xcv, mean=mu, cov=sigma2)\\n\",\n    \"select_threshold(ycv, pcv)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Multidimensional Outliers\\n\",\n    \"\\n\",\n    \"If you completed the exercises above correctly, the code should return $\\\\epsilon \\\\approx 1.38\\\\cdot10^{-18}$ and $F_1 \\\\approx 0.615385$.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 7,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stderr\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/ipykernel_launcher.py:15: RuntimeWarning: invalid value encountered in long_scalars\\n\",\n      \"  from ipykernel import kernelapp as app\\n\"\n     ]\n    },\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"(1.3772288907613604e-18, 0.6153846153846154)\"\n      ]\n     },\n     \"execution_count\": 7,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"# Load data\\n\",\n    \"data = sio.loadmat('ex8data2.mat')\\n\",\n    \"X = data[\\\"X\\\"]\\n\",\n    \"Xcv = data[\\\"Xval\\\"]\\n\",\n    \"ycv = data[\\\"yval\\\"].flatten()\\n\",\n    \"\\n\",\n    \"# Fit mu and sigma\\n\",\n    \"mu, sigma2 = estimate_gaussian(X)\\n\",\n    \"\\n\",\n    \"# Choose epsilon\\n\",\n    \"pcv = multivariate_normal.pdf(x=Xcv, mean=mu, cov=sigma2)\\n\",\n    \"select_threshold(ycv, pcv)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"## Recommender systems\\n\",\n    \"### Problem formulation\\n\",\n    \"$r(i,j) = 1$ if user $j$ has rated movie $i$\\n\",\n    \"\\n\",\n    \"$y^{(i,j)}$ = rating by user $j$ on movie $i$\\n\",\n    \"\\n\",\n    \"$\\\\theta(j)$ = parameter vector for user $j$\\n\",\n    \"\\n\",\n    \"$x^{(i)}$ = feature vector for movie $i$\\n\",\n    \"\\n\",\n    \"For user $j$, movie $i$, predict rating $(\\\\theta^{(j)})^T(x^{(i)})$\\n\",\n    \"\\n\",\n    \"$m^{(j)}$ = no. of movies rated by user $j$\\n\",\n    \"\\n\",\n    \"Learn $\\\\theta^{(j)}$:\\n\",\n    \"$$\\\\min_{\\\\theta^{(1)}, ..., \\\\theta^{(j)}}\\n\",\n    \"\\\\frac{1}{2}\\\\displaystyle\\\\sum_{j = 1}^{n_u}\\\\displaystyle\\\\sum_{i:r(i,j)=1}\\\\left((\\\\theta^{(j)})^Tx^{(i)} - y^{(i, j)}\\\\right)^2+\\\\frac{\\\\lambda}{2}\\\\displaystyle\\\\sum_{j = 1}^{n_u}\\\\displaystyle\\\\sum_{k = 1}^{n}(\\\\theta_k^{(j)})^2$$\\n\",\n    \"\\n\",\n    \"### Collaborative filtering\\n\",\n    \"Given $x^{(1)},...,x^{(n_m)}$ we can estimate $\\\\theta^{(1)},...,\\\\theta^{(n_m)}$. Given $\\\\theta^{(1)},...,\\\\theta^{(n_m)}$, we can estimate $x^{(1)},...,x^{(n_m)}$. \\n\",\n    \"\\n\",\n    \"Guess $\\\\theta \\\\rightarrow x \\\\rightarrow \\\\theta \\\\rightarrow x \\\\rightarrow\\\\ ...$\\n\",\n    \"\\n\",\n    \"#### Collaborative filtering algorithm\\n\",\n    \"\\n\",\n    \"We want to minimize $\\\\theta^{(1)},...,\\\\theta^{(n_m)}$ and $x^{(1)},...,x^{(n_m)}$ simultaniously:\\n\",\n    \"\\n\",\n    \"$$\\\\min_{\\\\theta^{(1)}, ..., \\\\theta^{(n_m)} \\\\\\\\ x^{(1)}, ..., x^{(n_u)}}\\n\",\n    \"\\\\frac{1}{2}\\\\displaystyle\\\\sum_{j = 1}^{n_u}\\\\displaystyle\\\\sum_{i:r(i,j)=1}\\\\left((\\\\theta^{(j)})^Tx^{(i)} - y^{(i, j)}\\\\right)^2+\\\\frac{\\\\lambda}{2}\\\\displaystyle\\\\sum_{i = 1}^{n_m}\\\\displaystyle\\\\sum_{k = 1}^{n}(x_k^{(j)})^2+\\\\frac{\\\\lambda}{2}\\\\displaystyle\\\\sum_{j = 1}^{n_u}\\\\displaystyle\\\\sum_{k = 1}^{n}(\\\\theta_k^{(j)})^2$$\\n\",\n    \"\\n\",\n    \"1. We start by randomly initializing $\\\\theta^{(1)}, ..., \\\\theta^{(n_m)}$, $x^{(1)}, ..., x^{(n_u)}$ with small random values (symmetry breaking).\\n\",\n    \"2. Minimize cost function.\\n\",\n    \"3. For a user with parameters $\\\\theta$ and a movie with learned featurs $x$, predict a star rating of $\\\\theta^Tx$.\\n\",\n    \"\\n\",\n    \"#### Low rank matrix factorization\\n\",\n    \"We can take $Y$ as the matrix of all ratings. We can get the predicted ratings in a vectorized fashion using $X$ and $\\\\Theta$ by $X\\\\Theta^T$.\\n\",\n    \"\\n\",\n    \"You can find related movies $j$ to movie $i$ by finding movies with a small value for $||x^{(i)} - x^{(j)}||$.\\n\",\n    \"\\n\",\n    \"#### Mean normalization\\n\",\n    \"We substract matrix $\\\\mu$ with the average ratings for each movie from $Y$. Then for user $j$ on movie $i$ predict $(\\\\theta^{(j)})^T(x^{(i)})+\\\\mu_i$\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 8,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def normalize_ratings(Y, R):\\n\",\n    \"    m, n = Y.shape\\n\",\n    \"    Ymean = np.zeros(m)\\n\",\n    \"    Ynorm = np.zeros_like(Y)\\n\",\n    \"    print(1, Ymean.shape)\\n\",\n    \"    Ymean = np.mean(Y, axis=0)\\n\",\n    \"    print(2, Ymean.shape)\\n\",\n    \"    \\n\",\n    \"    return Ymean, Ynorm\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"In this part of the exercise, you will implement the collaborative filtering learning algorithm and apply it to a dataset of movie ratings.2 This dataset consists of ratings on a scale of 1 to 5. The dataset has $n_u = 943$ users, and $n_m = 1682$ movies.\\n\",\n    \"\\n\",\n    \"The matrix $Y$ (a num movies $\\\\times$ num users matrix) stores the ratings $y(^{i,j)})$ (from 1 to 5). The matrix $R$ is an binary-valued indicator matrix, where $R(i, j) = 1$ if user $j$ gave a rating to movie $i$, and $R(i, j) = 0$ otherwise. The objective of collaborative filtering is to predict movie ratings for the movies that users have not yet rated, that is, the entries with $R(i, j) = 0$. This will allow us to recommend the movies with the highest predicted ratings to the user.\\n\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Loading the data\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 9,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"((1682, 943), (1682, 943))\"\n      ]\n     },\n     \"execution_count\": 9,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"data = sio.loadmat('ex8_movies.mat')\\n\",\n    \"Y = data[\\\"Y\\\"]\\n\",\n    \"R = data[\\\"R\\\"]\\n\",\n    \"Y.shape, R.shape\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 10,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"'Average rating for movie 1: 4.52067868504772'\"\n      ]\n     },\n     \"execution_count\": 10,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"'Average rating for movie 1: {}'.format(np.mean(Y[0, R[0, :]]))\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 11,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"<matplotlib.image.AxesImage at 0x1244da860>\"\n      ]\n     },\n     \"execution_count\": 11,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    },\n    {\n     \"data\": {\n      \"image/png\": \"iVBORw0KGgoAAAANSUhEUgAAAYAAAAD8CAYAAAB+UHOxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvDW2N/gAAIABJREFUeJztnX+w3lV959+fTSASqgIqlFxwk2ikk4Lcmlx+pGUnDa1B1inpjNuQ2Bosnewu2trirBdadu3u4tTsdrB0rFQWMLo0Max1McO4ZmyQLR0oJLFPBINIeqWQGzBWkLbGTUn87B/P99yc5zznnO855/v7eT6vmUye+/2e7/n983M+53OImSEIgiCMH/+i6QgIgiAIzSADgCAIwpgiA4AgCMKYIgOAIAjCmCIDgCAIwpgiA4AgCMKYUvsAQERXEdHTRHSQiG6qO3xBEAShD9V5DoCI5gH4NoBfBHAIwB4AG5j5QG2REARBEADUvwK4BMBBZp5h5n8G8HkA19QcB0EQBAHA/JrDmwDwvPb3IQCX6g6IaDOAzQAwD/NWLMTrAACnL2dMzP8RAGD2+GmYmP8jfPsbC5MicWzJaVjwnR/lvjt9OeOHB2jIzas/eTpOefGHzvc+3vb2o3PxTvne5PTl/RXcDw8Q3vb2o5g9fhpe+tHCgfT50mvzzxcnM/7/9PzpoH88OvCdHp76za9diH9+I2PBd3408F7FOSQfVBgqDqocXPHWn6nftrzwpdl0r/7Oy9NjS04DAKubvDzW06U/AzBX71S+h3wbUs9e/cnTccZZ/4QfHqAhP/LagUKvG3VRpA2pMiyrTdrSb/NPhava7ks/6n8TUy/zwv5HvPz3zPymvO/qFgG9B8BVzPwb2d+/BuBSZv6gzf3r6Cy+lK4EAOw63Jt7vnbR5Nwz9TsE5V7/X/fP9NPm/1TvBABgz+Q86/ehYee5C2Vm2ySWbuwNxMX0Y3Z6FSa2PBIUls8fX3yneiewZ3Le3HPzb92tmccqvDzM71Xa9Xcz2yaxfvm+oLCneidw69lPDIWvu5nZNolnVm+1xluvQxfefsNQHqs80P0w/beh0qW+33W4h1uOXDT3e9lD182lOxYzz1Ta9fJSdfzWs58Iiqfy65YjFzm/ia3XLvR4hvqpx9NGkbjpZQTE12OVZ+pbWx3Li7+Nv+Av7GPmlXnu6h4ALgfw+8y8Nvv7ZgBg5j+wudcHgDI4vmYF5j+4rzT/UgqmLnxptXXOoahv1aCS4pevEfsao2sgqxLXgGIyO70Kxy4+aq0PKYN6SJg+ipRxKCH1v8p4lN2eQymz3U/1TuD+7VfM1esig5H+begAUPcewB4Ay4hoCRGdCuBaADtDP951+ORMV0fNWFx/K1Rl0d+73AL9grb5PbOtn8kplSAvrmb6dh3uzYXn8k/5oft1+W2PD/hnC8eVdl/+qMa8bsPDA8/1OE71TljLST3bcWCF81tf5T928VFrnPRns9OrrHH35aP5XP9u/fJ9Q/FV/unfTmx5ZKg+zGzrz97UDNv81seeyXlDZeurq7bv89Drsu6/euardzpmXtjiYatTef6bdcpM/3enFgyEHxLH2HDUb/17Vc6m25B4mH7uOLAC6zY8PPfMrCu6+zxSBo5aVwAAQERXA/gjAPMA3MPMH3O5LXsFIAiCMA60dQUAZv4yM7+Nmd/i6/zbwMy2yYEZZZcInb0VQZ+ZhIQXOgMvgsuv42uGZ/FFCJ2VlZW22elVtZRpDG2LTyoxK6sqSOljysr7Tp0EtolkiuLzb/3yfUOijhj0TkdfatfB+uWD4i59eRpS4ULc6GIGlzgsZFn8zOqtuW7yUOl0xWP3vXcXDkNHbdzlUZas+MkPfarQxq8NV9m4xIYmC/aXq/FTd0es8qWsPYrU+Kfsa6n2XZRODQBmolNnlDGjp03+G1rQ+gZVVZvF+qCox0tVaqWFcuHtN8y9O3bx0cKNLVTeqcsl1y/fNzSIT/VO4JYjF839nbff4fpblVPKzMhXj2a2TVrTGipvVenN23fSw7CVp+u7EPR2o09K8tJgq/s6vj2ZqigrT4CTbbLJlYyqH7FxKGvQav0AoFdYs0K6OtW8zlZ/78rImW2T2HFghdWvlMwPrai2zkavHGZFWbqxNxef+7dfYfXTTEOIhsk5e45Zn+ubVT5ss8g9k/MG4qs2wfRydc0qbfnnS0NMx+CqL+uX78PSjXatjJABUGmLmPXWVJcFBvNTH7wVF95+w4A/LpGWLd36akWflJibnwoVl7x2pMrKttHrIlWkqqtf69jyMhSV/jJWoEUw+5mUASl1IKx9EzgG2QQeTZpQ5xSEcaK1m8ApKJVF1+zBpxZowzej1rFtvOkigZRRN290921W2tJvzuLM723qnnlx8OW1a9boygtdpVC50fdVQkVJwMm8Uf7oabWpFuq/fWXmioNN/KP8zIu3ynfbHowNPV42VVazHH1x9uFbOZh5lKdaa9aR0D261LjnqS2ninLMehKqJm6GHbu6USJGMxxb/tjy2haPWFo/AOinINdteHguI/RMsokCzE26PH16G09+6FNDz5Zu7M3JrPM2Ak257q7DPTyzequ3M/AdbLHNmk1xlvn92kWTQyIIteR1VRo9XWae6fLkW89+wro019On3K9fvs+aX8seum7gb99gbm7kqrMOwEnxoJ4felzViUpbHPQ9CD3+z6zeOhQ/3T9fnF3fudzr+acGyKneibl0qTaguPJXr3f678OsHyqteybnzaVJ5ZF+5sNWziqeqtP0iRb1NJv5rTBFMWbdU2cjzPjvOLBi7vCcK2zf+SE9XFfcXOjptfUXPpZu7PcHZppUHPTnpjKKmVehSgkmrR8A1i6aHMhk1QnaDkwozE1P5d4m0/Ttpq9dNFypVIVT7/PirtCPyMce2AiZbbpmiLZBR+WNq7GuXTQ5l895cmBV8Vxx1Cum6hT1cM38tW086iYQdDc2f1x1YtfhnlOeb+aDcnPLkYvwzOqtA7Nm28ah+b15UtTc6NbzxBZf216O2cBdEwVbefnaiWmSAzhZP/RO31ZXbIOTKyw9Ta7Oyux89bSo+q2bXVDfLN3Ys+61KPTBzRYnc7DW0+qr3+az2MFjqndirn/T424OwOZvYLgP0cOOWVW3fg/gTds/bK3URY+Bq8pUFy65dxny8Nij6WXJ4H15WCR/Xd/60pmXB740277Nq18hee4L0+V/3fVynLGVT0i5lmUKIs+fIuG00hZQLLIJLAjjQVN2fYDRHHRHahM4BdtSNHaTpsxTwKZfZZ9MLZvY+OVtUnWNvPSHiOWAduVDTFzqPpQ1/8F9jZ261zv/OssrT9Gijvzo1ACgN8q8Bmgb0WPFHhNbHimtQphhVznbKRrnXYd7wfGzafYA1R1809HrQKwBMx3bN670q0YZsv8z1TtRqtXIooRY7lSEdIpld5ZtUA2OPRNQpFz0g3Q2Y3N15EenBgC9UZZhWzyEsjuyOmZWRePs22A3sR1aCrHY6sI3sJt+6Jt3quGmmKTwaY+YKBPYIYRoxIS+r8O0sysMczPW9rxq6lqR6Hc8AHETzdgBUeWfuUm963CvttVQ6wcAPVOPr1kRbXI19p0Zdp5btSoJjdetZz/hrSgh2gY6up64rdKY+ugh6OqHrvDUb5t+/S1HLhqKs95QdFVec/bj06RQcfKlxWZSIQ9Xx+cKT1dHdJWNqhc+E8kuHr3xkqFnNvVHHV+HoX9rOxsB9AdB0488ExhmnGxxiDmj46vnt579hPOUvK7xFoPtTMfMtslgbR7TPH2eincM5uzf9LesAbH1A4COS4c5D/OgyI4DKwY6HvX/7PSqgYYdMptUuughKxLlt25P3KyEyx66zjvTNdE7E7WkNO297Jmch/u3XzHU8boq0Z7Jedal8FSvf4PW7PSqgfgCg6p992+/YqARmeGs2/Dw3OUVKv562bg6cX2mPtU7MWA2Qun5X3j7DdZ6oeehygfXASLzvgefCqTup94B7r737mh7+ipOys69+vv4mhVDOvBmfdM7DNuAZUP3Y8eBFUN67Hl1WlfJtHWmqr4ofMbXlKqsK8/WLpocis/s9KoB1V6zzun11Mb65fty+xCbTr5uvkO/XU797RvgzEN1IXtFtnemKm2qOG5ktYDKUNVyaQekaA0U0TRQaSlbW6Fo+nR3rvzOc1OlWQg9PJ+WiX6Tks+PFOpQuS3jW1s6q1RTrILYPFLx19Nh+lE0jSHtwnebXKy/ipFUA/U1VKE9FCknXyNua/nnxcv3vqqOvQ7VRtUJ1VUubRtwfKTmf1nlNjJqoPopV1227NuoMeXKLrsspgzPFbbtue6v73vTL93PUPm8z46NSqvur3ki2DSDkacxs+twb26/xQxTz0ObGM0WPzNO+rO8PNS/UctxXWRn4pJxm3lkPjefqTB1MZ3+LkQNVIkhbHFR6JZRbWkw80r/rZ++9Yl9bHlvlr1eR0wz2CH7Kup7V52ynVKP3Qw39ylUHPPakMukt16XXX2Cb69Hr7t6OwT8+zxm/dL9MU86q/jn7QHFbFzrJK8AiOh8AJ8DcA4ABnAnM99ORGcB2AFgMYBnAfwKM79MRATgdgBXAzgK4Dpm/rovDLUCMBNUdHap/6+baLC51y9sDvHbhT5LUr9jZ062MGa2TeKZ1VvnOkfzfawIQuW1aXvGRegsUDXcdRsedprZjsUWpl6men6p365v8kxLm/744qCe33LkIty//Qocu/gonlm9NbisbWIzPRxbfH1pCKkDtjTmzbj1vFbprXP1Nju9Cus2PJwbV6XU4HvvKt+YVUdsGpV7vfPX41AkzyoXARHRuQDOZeavE9FrAewDsA7AdQBeYuaPE9FNAM5k5unsLuDfRH8AuBTA7cx8qS8MNQCYHXcIMctul1uzYIqiV9iu42vweTL1PKNhdYuAYgaAlHiZ7/Pch9TzkMlLTD1LET2k7BukYsuzOkRPeRMG/XdKfMzB1jehiKkzlYuAmPkFNYNn5n8E8BSACQDXAPhs5uyz6A8KyJ5/jvv8NYAzskEkF31ZFLq8CVEnVEs2V4bHNIiQeE1secSpzubyJ89fc+kZ4meIyCUkParimtjyXmkmmZ1DiAhMuVMaUqGiszxRmJ4OG+qbvHqw7KHrrP66xCGphrsUuhaKi9jOXGnG5cXJJ0qZ6rkPvoWIKELqAXCyLinNr6InZ10mzlUYJnqHr+ezTf3ZhRmOyjdXmd5y5CJv/uhaQbWIgAY8IVoM4C8BXAjgOWY+I3tOAF5m5jOI6AEAH2fmv8re7QYwzcx7Db82A9gMAK/BwhU/R1cD6CfqwttvKEUcE0PTG0+mSqJJ3iolb8btCzdGbKHjmjWZ8UwtJ+V/nmgjVfulKGa4ebN1E5u4xyZC1CkzHaEzWTNMX13Li38eNi2uKjTI8sRFOmb6y1qRmPmY1wfYqG0TmIh+AsCfA/htZv4H/R33R5eoEYaZ72Tmlcy88hSc1IfWTRTn4ZvRhaI6LNuMtQghG2o6ytStC2Wq15U2/QrGGEI6f9eM2hdPwD9o+crInPnm1Qfb6WQzvj7roqGrEzPOZrp8nb9tQ1RfISi/9O/1wcFVT0NWji7U4GpDzz/zBLVvomGLv4kvzrvvvXvovTLVkrKKAk6mRc8LV+dva7emO995HR09PDOf1SpKz8e8PsD0M4ZCKwAiOgXAAwB2MfNt2bOnAaxm5hcyEc9DzHwBEX06+73ddOfyvw5roDPbJvHmu4YvUgGatVBYBWrGUseVjL7Zt23mWMVMKjQ+Ie9DKHMWXqZ8vSp1zSpNnKdSx75ADHVIEPQwVPorXwFk4p27ATylOv+MnQA2Zb83AfiS9vx91OcyAK/4On+FLt82VeHyvlOYpxT1b12dP9A/5WsLJzQOOrrKl6Jsex+22bgeRqiRKd8qRc9LXc1Rd2ezK6OrU+pH5ncdHp7d+DY2XehyYNvMLqbzt6lNmtj2asxBzKeS6sNs0Or/EENltjqgy5dDZsumqqhrladOnttm5iH+mxQ15Dezbfi0sM9f1+llm8qqCz2vbG59olvXKtOWPz436pAoEK8hWUQL6OcAPAzgCQA/zh7/LoDHANwH4M0A/g59NdCXsgHjkwCuQl8N9P2m/N+k6hVAnRonMauJMvcw6iImzkU1JxShM8268rOs2V6T+04xYZtuu1hvgXbFu0hc9LZUhxbQXzEzMfPbmXky+/dlZv4+M1/JzMuY+ReY+aXMPTPzB5j5Lcx8UV7nH0oRk7S+jE6ZhfoItWNU9ga2j6L7GToxcdbt6ChNjhTyOn+f7Zk8ysqblLSV2fmnWqhMcRtjGTNVbh9LyOy6LZ1/UWKvpARafhL4bW8/muum7plSSGUJqdyuASZEayWUvEM8qRo4Lv9S46WLNkLyTrnJE6G5zBiH+O2yhurDJqJp2nRBleH76mJeuFWd5zAxVZVTyjU17BDyFAiqptUDwLe/sRDH16zIvZ2pzJlsGf7ZtCjyOm5fZ6bLt5du7JWSHzsOrBgyWRwiY3c13CINK0RDBDjZWHQtIFfczYalLjoH/DcxKb/VZrlyq1uKdYXh057RceWzKo+88nXVJZtGiSuMFEztFb2TD6m/Nsq8Gc/VeerxfPNdJzXRbG00T0PH9twM28x3XxrLHAhDzKWbtN4Y3Af3rx6ZJdoo0vQ5CUEQhhkJY3DHlpw2oDseI/5ImcWbMwDbDn1IHHynQl0aRCHx9Rlvs+nk637GzrRc7s3Zj0+P3oyDiSpTX7xd/tr8MuuI74Snj+NrVkRraNn819Nm0yxy1RPbakPXbopBj0PZcnc9bXmaNnmEaF7lPTfzOi/smHyJEX266qAtjiFh2HDVndgybvUAcNZpJ/cA9kzOm9NlDiHUkJlOiJqdsh8OnFRLdR3rtvmtlnzmBR/mBQ82XJe0qIso1HvVGep5sPveu3P913FpLCmxS56qoIqLksHa1DNVmZr4yi51kzIvf/VyvPy2x+dUHFXcXegbzbo7pRaqDkvpaVK/dRv0imdWb8XElkcGZNdTvRNDl7WEsmD/wij1USUaMSdDOubEyDyxqpN3gt30Q52a9rk1wzLzU/2tX/hii9v65fsw1TvhvbxIEbNnp6fZPO+itwtVX1x5bRtYXYfQgH5Zh6r6KlotAlqwdIL/1bODN+iUoT5oEnNoqShKHbQsbZ8UA3N6mmLTp7vX0xCTntQ8NU0k6Kc2ixyccqkzxhxoKqueTPXCLdCmULXITs+z1IOUTYoVy2iXPj/yDs+Ftmc9DJufIyECMtEzRe8IbMRsxrmMmgH5M87Q0VaJVMwGEXLow8exi48ODIo+P9V71wwlBDWjVRUw5mCRK0ybH7Zn+oBvrghtF7ubnbqJKnPXpfDqAvi8g39qQ9S23A8tS70umo25iFJCqMhOhaPCchl909NkE7XocffV9bIVN1z++v5Wqz49rebKPA+zzH3GA2e2TTqv7ly34WEAg+3Zh+5GfWumJYTOrgBCaNux8DzUSL7rsN+2epexGfVLXUnUsepQhKwGylwF6OlKnUmnzGZd3+SZRfb5Y3NXZttMMT1R1ypDdfJl3SsSykisAC567fetz81ZjWkuQs1SbPbDlZsQbMf3zRmS6UZtxJjP81QIdx3uzY3kLvPUtpmXOaNx/Ta/9bm3hZ2Cbfa1dtHkXDrNMHYd7g2Y6vbNRoFBM+G2/NVnRD45uO6Ha8ao4qyXu14P1SrApjRg5rMrPa7nu++9O2pWquqhkqW7ZoZ6/io3rr2SPFv0Zjnondj926/I9c8sb9uK3JcHoatIlf96fbC1af23Hq5qc8qNrzwVt579BM7Zc8waJ5e5EDNu+h6a6c5cmcUoC7R6BaCbglCyUdvlya5RM280DZ3BzGwbNhgXegzefB4ywk/1TuDRGy/B/Af3Jc+UQi6aNv0uMitSla7orEqfzc1Or8KTH/pUUBx9cc9Ll9qcs+WzykegLyryzeRceRA7Q1XxtdWVkPqjvk+ZGaeuqsz9GT2f9HehdSxvHya1rtrahU3ubmt3qSuN9cv35e5XuUgtj5FYAejsmZzn7NBscjvfUlb/zsbs9Kq5fQGlzXH5bY8PuDHlxqY8XJ8J6TMk/cCUS4MGOCk/1RuOTcbs2utYt+Hh3JOwynytml3Ebgabv80B0ZyR5M1QpnonhhqY3ghdextTvRN4ZvXWgTDNsGyzJl2jQrdVrzOx5ZE5c7w7Dqywrl4UC/YvHKoXSu471TsxcPDON0tbsH8hgJN1R9Wf0M5foWadtnS5vgEG89lUpdXLUsUTGDZhrZejOoS36/BJrShTO8cMR6XTld+mBpWrnE1/lTaVXgZPfuhTc+3Xtyenpyl0lr10Y39VpcdXDc629mCGbx6w1A8nmt/qA0wonVgBFJnRCOVS575K18o7NL5dNDNetszc9K9rZR1DE9pkI7UCaMNJ0xAZbFHNhpSDPnVTpPMPyR99BhcrNqkD30w6NL7P/UZcPSnTXEIqtjboK0/XKsLlX12df4xmVoyfvnfrNjwcfLDQpZHmo0h6OrECiKGtmj9l7O53ceZYlKJpblKnPJW6yrlN9anuNNe54mgin0dqBRBDGzt/oBwrf1VXorpM9LqwzWSKptnV+VeV1jL8rauzKBpOmauumLj4tGVCw1Eb+3UQu+Krk9YPAKa9EfV3ir2WWDXQovZN6sBnd8SFEimY+bB20ckbilx+mY3PdiOY7W/fxq9NddBG6GalDZvlTte3IfnoqkvmprVtkzN0kKjqsJQN28Z02TfWlYXrPIIrv2zp0FV29fIo0rZd4fvMYbg2nvMoqw9qvQjoTds/3LklfNso63CJj9QldV1L8bKX4W0VNdbJKG/c1kGROpmX97WJgIhoHhH9DRE9kP29hIgeI6KDRLSDiE7Nni/I/j6YvV8c4r9+YMO0X18GoRtZdYRXxve22WVM5x/jv/5bX1LHpPHYxUedh9Ni4wa4V0S+hpa3iWcjpPO3Hb4zsaXXpx4c+m1enMqY7dcpRvGRl+a6Vuwx4cxsm8T8B/fNfROb/z515BgKrwCI6EYAKwG8jpnfTUT3AfgiM3+eiP4UwH5mvoOIbgDwdmb+d0R0LYBfZub1Pr9fR2fxD154w9jPtNqEa9ZSx2ZrFzd0BaEJalkBENF5AP41gLuyvwnAGgBfyJx8FsC67Pc12d/I3l+ZufcScpNTlbRBBa9NuGbS6qalKlGdv61M6pSXN01VM9q2yvxDKStfUv2J7SvasJdYVAT0RwA+AuDH2d9vAPADZj6e/X0IwET2ewLA8wCQvX8lcz8AEW0mor1EtPdVHBs4zaj/roPZ6VW5MrrQQmxDYbsoY5Az8yk2vTEduK1MTHv8MbS5bGwUNWrnouvy/FTTEDpFVpnKzHsoeZcp+ShrwpM8ABDRuwEcYeZSddaY+U5mXsnMK0/BglpUqFyNIs/mC9COQ2pF+e7UgmC3rsrpMjsc2rn69ilCByhlTz0W3aRBWbgMmsXi08hKQb9HWRhu4ykHsXTKULYI6VPKUuoosgL4WQC/RETPAvg8+qKf2wGcQUTzMzfnAZjNfs8COB8AsvevB2A396mhixbMjqosXW5XRx+i1hUahzoGitT8iJn56eWh549rU8rWoHyzF1sHrmb85nemNU7AnZYyTvCG+gcAV/7q9VbroED+7E1Pl7r3oKwZ3/E1K6x1sQ2DQkoa9W9CNt3z8N0Nkhe2y+qq67vZ6VVRNppcYRcheQBg5puZ+TxmXgzgWgAPMvN7AXwNwHsyZ5sAfCn7vTP7G9n7BzlgB1pfAZjX4uWZqE15pxMyysZuUFd52MoXl7L2MlRnbF58YVpSNJ+70m2WhU+zxCwPfdDJ68TLViTI80/lU8pMzZYHZc34XFeDpk5QQjW4XN/opKTRVgdT7kDQf4fmhRn2/duvCKpn6ruJLY84Tb8r8+IhYRehioNg0wBuJKKD6Mv4VY27G8Absuc3ArgpxDNdDVTfEM7Dl0Eh9+8CaTfsuFD+KAucdePby7AdqMqbBdkO47jeAYPp1i0cmuUUMjtVf9vK2GUp0UYZM8YU8hpvlatF3WpnGegHsELrdtlnUlLtdNkOIJp9Q8zKqIhqph7OLUcuSjI7nULrD4Kdd9N/nMuMOg40jSO2ja+yVS6rKDubSmrK4Zoq1EvL8rOKuI3jAa7QNJv1tKt5NTK2gHTNH9M2dtW4NhRTNhrbIGONIbbTceWJSnfRsrPN7G0dvUtpwJf/Vcy4F+xfOBfnIuK3KuLWxQ6tKKFpNicpbbRIWyatXwHEWgNNoY5j/baZadWzizpnL21enRWdRYemraw8MMttqndi4EYpQchjZFYACiWPr2ITtY6TxrbZalWds+0Go6rxdXxlGdtKpeg1lz5CbpiLxdwEVppAdRHaxkzb+rEmL9pCUzP3vD2oOuLVmQEA6G8ymdYW88QxNts15nV0rgveXZVWLelTBySl2x17ObjtvW6N03btoSt81zd5F12bFhRDLKyam4MpmiMmeuPQRSwu/fsUy7EL9i90pkvF23dlpcrf2elVXjGQeSXg+uX7hq5fDNGi0uulL0625/p7/RrSUNTqx3W9obI068PWDm3hmH67/FFqlnlWfWMH1zIuh9Lf33r2E1YbTeuX74sqg5S21BkRkK3BxZIi6gkVH4Qu//U4hMbH504v9Dw3oWnfdbiHW45chFvPfmLoGxUX08+8dOnufW5jxCi6W/238jNVJKOn0YyvLc6+6w1tcciLV0i8lZvYOq2bTtbL11VmvvdmPHcd7mHZQ9flthdXnPPSYoZ3fM0KXH7b43OaO75v89qQeSe0me6QfE4VJZvaSDPb+hfJ63U7TwRo1sFQEVBnBoAyaIOcehzMCI9KGl31pcqJhC/cNpAXt5C8KTt9bcmvlHhUFfeR2wNQFycUkSWmZHQbdvZjZLK2b2PzTOV1yJI9NH/0eJgioFA5skmonr/+u4zle0jnb4pvYsQMdWi7pZ590NuQTYQakjeh53BMbGVYdgeaekFLKvosX49DLCkXDgEdWwE0MbPsgj58Hinis1TRgvnbZHZ6FY5dfDQpT0N0tF3lVfWsvUyaCLdIvVTxDc3jtszYy0blQ0z6lLi7/cEpAAAgAElEQVRVd2/7Pq9OmN+M3AoghryNuxgW7F8Y9F3qZnBRf0O0o9YumoyS/wP904ghaVIzD31WZ5vBKnfHLj5ayOCW2hyd2TZpPXmpN5K8TcjQmV5s2ZqzMd+Gvy0Oefkz1Tth3VROMUBnOw1rMju9yhpPM023HLko6CrRssU/IYTa3DH9C92813GZRbE9U52/Hk5K/ujtL2YF05kVQFWzBp+/ZYdZ9rWEwOCmniuu5uZc6CajbRM4BNtMcHZ6FdZteHgorkVWdXmzoqIz6ZQZHWBfccWkM+/8RhXnO3Q/Q/3X8zcvr/T0p5RLFW0nhJiyL2vlFrPx7GLkVgA7DqyoRDZnFm5VMxWgb4irKn1oX1zXLhqsmCHpCu38Q2ecE1semQtXn634bAqZmDJg10xZvS/aGJdu7M+oY2Xy+opLqSrH2IDKu2rRPCRmI2Z/xPQzdHDR81+JgFx1Sy/nlHKpq/M388W2X+HKc9fq04dNdVvlVYzdptR+pTMrAKE8iqi0hcyIYtX5hG5Shw2pEKQ+DTNyK4BUYlYNVV6JZ4tHiKZNalg+2WXIzN7lxicuc31rprGKxpp3uXZM2eqHsGKoUnukLs2UmHDMGe9UL9yUcpl0vfN31bc6rugc+QEgpnLYNEpsHWlKwdiWknsm51VSefdMziu0ZPZ1fq5392+/wvq8rtmZutXLdW1ojMw8xPSCbclt09wo6x6GugwhppZVVXW5SmztuMhAW0S11lbf6jDlIiKgHJrafBLiUKIHlwiiKZXOtoQvFCOk/NrUV4yUCMhmJyNmtDU3D0MPHs1sm8Tltz0+9Lxuw1Z5G6O6KOn4msHNcp8Kos/P2FWOGUfz0JdrmWvGNyQM05YTcHJDUr/fV0+DT7XSl1Yzbj77UTrH16wYWAHoFxvlpddm+rqKmanZDnQbOq7yMutW0bjppB66zLvEyLUKs8U/ZINXR6/fl9/2eJRYV6ntqn/68zzKOqAqKwAPTVwG0YZZRMpstc6NOFu5qGdV5V9sXQg1NJaXb7Jy6A4pdcRUoy2LWmwBEdEZAO4CcCEABvDrAJ4GsAPAYgDPAvgVZn6ZiAj9S+OvBnAUwHXM/HWf/7YBoM6OpsuNr+6BJDU80eAIo8t1sa109bavEOoSAd0O4CvM/FMALgbwFPp3/e5m5mUAduPk3b/vArAs+7cZwB0Fw/YSok9uikdMOyDrl+8rTdxTZJkccorR9N+8GatqLRJTVGaLsy2uIQfSQt7ry+mQU6uhYeZpBKWKJV3o6dDD0EVIMWGZ+WH6a3MfKtox/YrVtHKFYXtmigr130rEY5ZVXvwntjySrPEV4r8NW/z0/LadVneVny0+sf1V8gqAiF4PoAdgKWueENHTAFYz8wtEdC6Ah5j5AiL6dPZ7u+nOFUbTIiChXcgsWBDCqGMFsATA9wB8hoj+hojuIqLTAZyjdeovAjgn+z0B4Hnt+0PZswGIaDMR7SWiva/ipEpfqIXKpoixitlmyoifyw9zA9Xm1he+2fm3tS4UpepLQMr4tghFZ85lk1qPbKd4u0aRAWA+gHcAuIOZfwbAD3FS3AMAyFYGUUsMZr6TmVcy88pTsGDuuTpc1FZ5cejMNOZ4d1nELA2VDZIiDc6VRqWJ4zuIFmP7JMU+TwxtMAWeRxHruFVY1q2qE6xy5Ze3Ce/CzL9UM9dlkFpXiwwAhwAcYubHsr+/gP6A8N1M9IPs/yPZ+1kA52vfn5c9C6aJzr/sCl13Gma2TWLP5Lyoxh5yq5MPVxptz1ONzZn4ZMqp4RTJg9npVcknOdsi5kqp+yH1O+Q0eQplDdi6PzFlUdbkzrU34yO1ziQPAMz8IoDnieiC7NGVAA4A2AlgU/ZsE4AvZb93Angf9bkMwCs++b+JMm9Q9zJLXbtXFinxj9mMM7FVjLzOcunGnrPzMsU3ZZtMCPFPdeZ6HFWnYruwJJa8jdIQ8gy6KdosEszrzMteIRWdHJUxcJr7TDHt1Rb/lDyypSNEnTiFomqgk+irgZ4KYAbA+9EfVO4D8GYAf4e+GuhLmRroJwFchb4a6PuZea/Pf3MTuMtqW13ZwKxSLTM1D8xyL7seVJHmNpf3OKrehpZHm8stBrkT2MKo3FVbJapzqKKTKOpn18pvVDoTF6npG8cBqG5GyhQEkGbSwEUdVvZM8kwHlEGqDXIdmyjFF0bMEle/BMaFLw1m56/7E2v/PvRdEUzdfVt4troYmpbUfCwL1fm7bgxzUfYeQBERaRPk3RJWJ50ZAJZujJv92TJUfR8qPrBpz6RW0tBLHlLs9ijMe0VdfoZsVrnsp5jX3fn2GFzo5WgO7D6rl6a/tktGXPJ7n4aGr0NypSWvnGa29S+FUR28Hhc9vNC6qH//6I2XAPBvbLuuJXR1hikH2lTa1GU/MYfTbFSlReNapdjUkk1iJg6hA42t3PRnIflohjUWF8K0wU6OIAhC2xk5ERBQ37Vwo0DekXHAb64h1s8Ud2Z8XHEqg6qX2HmzNt+9AKYYqIj4xjTJEDObjy03FU4RcwqKMkW8TZKaBttKsQ46uwLQf5dtA17fbCxrw6orG4J5GjZlXm6eR8yKzywnX7m5yqIM7aIqNNW6vmlqy++mVvNNhNtEmCOpBdRkQ6g77K4MGEJ76frAUQWqXbXVqnBZ7X7kREC2AitjuZTnh1qaqbCLalfkfa+WkEUrgXnYqyqtkJhN0pTNrdjvXdQpXrBtRMfEvayystVZPW62i2cAv7hKsevw8GHB0PaYurFu+y62D1DtyqUw4YtfHq64xLRlNTilhhVLZ1YAU70TePTGS2QfQBCEaMZtRT1yK4CiF50L3aCLFhV9xOrIA+3TWx8Fxqnzj6EzAwBQf8MI0Zkum1g7Oa4LUOrAd6ApRIygcOnIx6DCTznkV1V5zmybnNORjwm7qc4qth7FlHEbybtLuK7wm6QzIqAy6Jopga4ybsvtsgnNP199rqMMZqdX4djFR1tf1uNYH0dOBATEzVBss5OYzl9ZHi1rlK7T/ESVK4IQnf3YxlbGtYq2/A29Ss/3XROE5p+vPtfR4U1seaQVHWuZ5VWkvRfpn5paDYzVCiCVcZpBdGmVNKpqjl22eivEUVV7G8kVQFOMS+cPVHNLlIlvphSjrlll56/Ho+gMs+uychdtkGHrNGHkMQU933wGDuugUwNAlxtSmytnlflq6yR8HffaRZOFOpaUtJjfTPVODDRMW3xjGmqM9ppt9j+zLS5P6uqYzYlR0wOCb9XUdNx0fBNKdSVrXXRqALj8tsdL8SemMy6rcwxd0jcxyMV0UKENqciBtiIrrud+wz5b98Xb/KYs0x9A/MBvqydLN9qtrrpoasXa5pWyL26uA3GxxK4UXXWjThFsp/YARDYqCNUwjm2rCbMQdVHLHgAR/Q4RfZOIniSi7UT0GiJaQkSPEdFBItpBRKdmbhdkfx/M3i+ODe+cPceKRFcQBAfj1vkDdrMQ40byAEBEEwB+C8BKZr4QwDwA1wLYAuATzPxWAC8DuD775HoAL2fPP5G5i2L3vXfP/a5LVNIm2WGXaFqV0qTNezDCeNKGOll0D2A+gNOIaD6AhQBeALAGwBey958FsC77fU32N7L3V2YXxQej32RVl1mINss120zbZlXjOMMV2o2qk00qtyQPAMw8C+APATyHfsf/CoB9AH7AzMczZ4cATGS/JwA8n317PHP/BtNfItpMRHuJaO+rGBT5qKvwBCGWtq1I6mSc0x5C0zPxJm2cFREBnYn+rH4JgEUATgdwVdEIMfOdzLySmVeeggUD73QRkCDE0LYVSZ2Mc9pDGOfVYRER0C8A+A4zf4+ZXwXwRQA/C+CMTCQEAOcBmM1+zwI4HwCy968H8P2YAJc9dF2B6AqCIAg6RQaA5wBcRkQLM1n+lQAOAPgagPdkbjYB+FL2e2f2N7L3D3KkDuqb75KZjCAIQlkU2QN4DP3N3K8DeCLz604A0wBuJKKD6Mv4ldzmbgBvyJ7fCOCmAvEWBEEQClJIC4iZP8rMP8XMFzLzrzHzMWaeYeZLmPmtzPxvmPlY5vb/ZX+/NXs/Exue65RnHnmqnLb3s9OrnN/lbar53rveqef6MXDT1v9U78TQ9yFqquqbGPvnNs2EmHT5jrOnXiXoCle/dCWlzMx8Nv0octVh6Aas66rG2Hj4rk0MMTGg15G8uOedoLX5YbrT670vvJSN2jI3d812mYrtulDX+1DtoJRrRxWdOgl8fM0KuRVMEAQhh5G0Bpq6AhAEQRCG6dQA0GXK0MVu86lkc7mt0tukDnrecrsMmtYhb5JRSXsbzkk01bY7NQAs2L+w6SgkE6OL7aoMbT2VvOtwb0iXWqV3z+S8WjoKM89mp1cN5FdVeWemu02dYmxcfPteNvS0x3ZgTXV4tjyxtc2UfcOYMIHBgSelfs5sK246ulN7AG23WNil27RSGYc0CkLXGck9gGMXH7U+r3IJF2PXXe8YzdlUmTPDqmyHhMwmYjv/umZ6thVAE7jSe3zNitxyKzuv2iwy7AKxWjhlu00lJoxOrQBEC2g06LL9dVkBnaTtK3Ifo37P90iuAITRoKudP1DvbU1tp6udP9De/bS66dQAIMbguk2TIgkl3mqDxseo4Dt0ptOmjXFhkE4NAEVnX2VcttzFDiQlzvo3ZV1S3eSsS9WdMlYfeflRNL9iTh673NZxsfiOAyuGwreVcehKITbOXd3j8KXT9a6qfqdTA4CNmNlF7ADiUhlLqXh58fT5WbTw8zo922aX+mZm2+TQ5naZuDbaYtM8s23SuxHsy9/Y8ly7yK9+p+eX8jt0Q3GqdyJ4oNwzOc/ptuhkKSRPFuxfWNqgbtazEMywyxgQUlUrY+qaSqetLbnyoCqxaac2gZti1DeMQgjd8FMbvE3nmbnRbMZnHDZzu7RJW1d9UeGkhtd0vQ5lZDeBQ0fnspaHXSnwGGJm1yofVUdiqraasxjV6T6zeiuAtOVuEfcqfuaMySzDoqsa9Y3v26bFhV3p/IH6xIMqHF94vr7D9V1XxVGyAqiZvJlnysw0dpCqQg2zrIEy1Z8iaWrbIN+2+LjoSjzHkZFdAdRJFTO4vM49RSwR2whDOsqQ2bbuJnYAsv0u4k+RAa1tFw2Na6dax8Z120ntc1K/G8kBIC8zQpdrKZunPqZ6JwYqeVknelPuHwD8Dc61UaV/EzNY2eKx63CvUMedZ8PFlXYz312HC1Xai2pRdYG8NmFLT8xAVWbnXtVJeGD4zo2UeBdJq6s95PmpfxdT93JFQER0D4B3AzjCzBdmz84CsAPAYgDPAvgVZn45uxrydgBXAzgK4Dpm/nr2zSYAt2Te3srMn82LXNMioJBNtNBlcN3L5S5tAJqkiMGmeiew40C/Y4jN55S86pL4o6y4dvkEtw1lWaDOthJTFkUsH5QpAtoK4Crj2U0AdjPzMgC7cfJ6x3cBWJb92wzgDmBuwPgogEsBXALgo0R0ZkDYrUXNmEILs4rOwjcTCqnQsSqKsXFwhedCzXKWPXRddDyUSmRKPoc2fn015AqnjWKMsuqe3vmXeatbmeRt6OvvVeeql3/VK7eYsqjD7E3QJjARLQbwgLYCeBrAamZ+gYjOBfAQM19ARJ/Ofm/X3al/zPxvs+cD7lw0vQIQBGG0aNPKuMoVVdWbwOcw8wvZ7xcBnJP9ngDwvObuUPbM9TyZtsw4hHbQxvogJhDaR1s6fwBzIssmKbwJzP0lRGm6pES0mYj2EtHeV3HM6W7pxt7ccruNy+6qiFmi1rERabvMPhb925QzCkD+0toWv7IGDVec29TZVEGVp9djSK0zTWOrs7Hx0+t1ShsUEZBQG13aOBWELlO1CGgngE3Z700AvqQ9fx/1uQzAK5moaBeAdxLRmdnm7zuzZ63GtYRPWdpXpbrWlhlNSJ64On8RlbSPIjN4X3m63jV1cVCT2PKiSPxmp1dFl1uIGuh29GfwbwTwXfS1ee4HcB+ANwP4O/TVQF/K1EA/ib7W0FEA72fmvZk/vw7gdzNvP8bMn8mLnKwABEEIpU0bvE0TugIQUxA1MEqij3EwoiaMLuq8SJ3tMUafv6y+QkxBlEBZy8WlG3uVbYrVfeLU1fm3aWldlDLSsutwL+hUcgxtO13cxTuMbSa0qw43r/MPOV9SFbICqIk23Wdcx4qkTekFurMKG/UVlqsculI+bUedLZAVQMtoU2dYR0OLTW/Vqryp5n/rpuzLd1L9CPnO5ca3Uqlb9NI0et06vmZF5au42INlYzUAiLZJPk2dqUiZ9ZbVmNYvr25wzoujLb9VPS1jQzPVj5DvztljP6eTcrq1ioFBTULqEp3lGcyb/+A+Z940NViJCKgmZInbLE2IpEbNeNqoMcptUkRALaPuitb08jc1/KrEMU2I4FI7/7Zt9rro+op6VDv/GGQAGFHq7vBCbeznkdoo8waOJuT8qWF2ZdUgOvfdZ6wGgK7PWNpMaIdfVRnkDRxNzPZGfYbZps1zIY2xGgBkxtI8E1se6YyIQxBGnbEaAMqgbZ1Xk6uaVI2hrog4qqJtdSiVslc4XcyXonE2vy/iX8q3ogUkCIIwYogWkDDyiAy6WcbpHo6qMPOw7lXQWA4ARVUkqxS7jMpGta1zKFs1VRdBqMHA1YDKHiyq7PxsdaCN4pFRNFlR56RiqndiLg9V26hbPCoiIEEQhBFDREBCIbogXhlVEUTTh/hS6UKdEQaRFYAgCMKIISsAYawY1dWAoo17ADLj7z65AwAR3UNER4joSe3ZfyeibxHRN4jofxPRGdq7m4noIBE9TURrtedXZc8OEtFN5SdFGGfauCHpE+XEDlhtPDsxiiedx21QC1kBbEX/jl+drwK4kJnfDuDbAG4GACJaDuBaAD+dffMpIppHRPMA/AmAdwFYDmBD5laogKKVuIuaSEXS3ITMvW0D1uz0qrHr/Gz1fNzuKwjaAyCixQAeYOYLLe9+GcB7mPm9RHQzADDzH2TvdgH4/czp7zPz2uz5gDsXsgcgCGnUcbPYKJtT9tEFM9917gH8OoD/k/2eAPC89u5Q9sz1XBCECqhjhTGOnT/QTnFcKoUGACL6PQDHAfxZOdEBiGgzEe0lor2vwn7jUF2UufFW5ybezLbJViwvx5k2btqWzbiJjKqiyXxMHgCI6DoA7wbwXj4pR5oFcL7m7Lzsmev5EMx8JzOvZOaVp2BBavRax/3br6gtrKUbe626g3gcGaVZoosurgDauL/VZD4mDQBEdBWAjwD4JWY+qr3aCeBaIlpAREsALAPwOIA9AJYR0RIiOhX9jeKdxaJePWU2Ypsp6nGYJQqjSxdXAGISfpAQNdDtAB4FcAERHSKi6wF8EsBrAXyViHpE9KcAwMzfBHAfgAMAvgLgA8x8gpmPA/gggF0AngJwX+a29VQpShmHWaKirs4iJZw2zgq7QBdXAG1kZttkY4OpnAQWonBpfjRx6bpO3RopdWjZCN1idnpV8gqj7PYTqgUkA4DQOEUajiAIw4gpiI4yjto70vl3U57eRbqQz3WKJGUAaBm777276SiMJG23FdRFeXoXOlOTtuaznpd1TohkAGgZTcuVU2cfTa9c8jqjqvK16XQ3SVs7066g19mm8lIGAGGA1NlHyAZW6IwxZbbeVAPq0nkLUTtuF+uXl193YtuODABCbYR20imz9S6KI+qm7WrHTZWhPjDWKX8vszxU3sW2HdECEoQSEfVQoQ2IFpAgNIB0/kKXkAFAEARhTJEBoKW0VaZdpTrlqG5ShmoKjWr6hfYiA0BLaauKXZUijrZvUqYwO70qWFOoy+lv64SlCzRpi0oGgI4jDa/dNH3Kua5VRVsnLF2gyToiA0DHkYYn+OjyqkKoHhkAhLGl7eYhiiAmroUQZAAQBhinjchRVtlsWvRUJuNUJ31UYXZEBgBhABEZCG1D6mSfKsyOyAAgCEISooDQLlJWSiFXQt5DREeI6EnLuw8TERPRG7O/iYj+mIgOEtE3iOgdmttNRPRM9m9TdEwFK9IIBSGcUd4bSVkphawAtgK4ynxIROcDeCeA57TH70L/IvhlADYDuCNzexaAjwK4FMAlAD5KRGdGx1YYQrSA2s0oy6+7WPfWbXi46Si0itwBgJn/EsBLllefAPARALo1uWsAfI77/DWAM4joXABrAXyVmV9i5pcBfBWWQUVoFymzpaZnWG1bEYn8ul3cv/2KpqPQKpL2AIjoGgCzzLzfeDUB4Hnt70PZM9dzm9+biWgvEe19FcdSoidgWGMgpmNUs9Y8TRKbGqXvm6YHBxddm6W3bZDrEqOkHVUG0QMAES0E8LsA/lP50QGY+U5mXsnMK0/BgiqCGAtMjYGY5XrorDVWjbLKxqc68RSxRNdm6V0UvXSJrk0IipCyAngLgCUA9hPRswDOA/B1IvpJALMAztfcnpc9cz0XhFLoWicutJdxqkvRAwAzP8HMZzPzYmZejL445x3M/CKAnQDel2kDXQbgFWZ+AcAuAO8kojOzzd93Zs8EQRCEhghRA90O4FEAFxDRISK63uP8ywBmABwE8D8A3AAAzPwSgP8KYE/2779kzwRBEISGCNEC2sDM5zLzKcx8HjPfbbxfzMx/n/1mZv4AM7+FmS9i5r2au3uY+a3Zv8+UnxSh7cjmZTqjbLdoVGirkoMPuRNYEARhxJA7gQVBaCWyEmwPMgAIglArosbaHmQAEARBGFNkABCsVGF7vMmlfxc36JpCRDRpxB4ga0M+yyawIAjCiCGbwIIgCIIXGQAEYQSpw55NG0QYo0bddohkABBKoYo9AyGdOuzZiDZP+dRth0gGAKEUTOujbbOoKJvAgjCMDABCJfhmMmUNDjHmEcbNDryIZ4QQZAAQaqesZW7sfQTjRB3iGVlVdR8ZAISRwjXzbZtIqinK7LTHbVWVRxdXXXIOQBAEYcSQcwCC0DAiImkHsvpzIwOAIFSEiEjawThd8RiLDACCIAhjSsiVkPcQ0REietJ4/ptE9C0i+iYR/Tft+c1EdJCIniaitdrzq7JnB4nopnKTIQhC3XRx01MYZH6Am60APgngc+oBEf08gGsAXMzMx4jo7Oz5cgDXAvhpAIsA/AURvS377E8A/CL6l8jvIaKdzHygrIQIglAvchK4+4TcCfyXAMwL3P89gI8z87HMzZHs+TUAPs/Mx5j5O+hfDn9J9u8gM88w8z8D+HzmVhBqQe7UFYRhUvcA3gbgCiJ6jIj+LxFNZc8nADyvuTuUPXM9H4KINhPRXiLa+yqOJUZPEAaRQ2OCMEzqADAfwFkALgPwHwDcR0RURoSY+U5mXsnMK0/BgjK8FIRaEJl4+xGjhYOE7AHYOATgi9w/RfY4Ef0YwBsBzAI4X3N3XvYMnueCMBKITLz9mEYLx53UFcD9AH4eALJN3lMB/D2AnQCuJaIFRLQEwDIAjwPYA2AZES0holPR3yjeWTTygiC4kQNQQh4haqDbATwK4AIiOkRE1wO4B8DSTDX08wA2cZ9vArgPwAEAXwHwAWY+wczHAXwQwC4ATwG4L3MrCEJFVH0ASkRe3SdXBMTMGxyvftXh/mMAPmZ5/mUAX46KnSAIglAZchJYEIQkFuxf2HQUhILIACAIQhJi66j7yAAgCMLYIBZaB5EBQBCEsUGtWuQ8QB8ZAARBGDvqPA/QZm2pVt8IRkTfA/BD9M8YCMO8EZI3LiRv3EjeuBmVvPmXzPymPEetHgAAgIj2hlxtNo5I3riRvHEjeeNm3PJGRECCIAhjigwAgiAIY0oXBoA7m45Ai5G8cSN540byxs1Y5U3r9wAEQRCEaujCCkAQBEGoABkABEEQxpTWDgBEdBURPU1EB4nopqbjUzdEdD4RfY2IDhDRN4noQ9nzs4joq0T0TPb/mdlzIqI/zvLrG0T0jmZTUD1ENI+I/oaIHsj+XpJdU3qQiHZkd08gu59iR/b8MSJa3GS8q4aIziCiLxDRt4joKSK6XOpNHyL6naw9PUlE24noNeNcb1o5ABDRPAB/AuBdAJYD2EBEy5uNVe0cB/BhZl6O/tWbH8jy4CYAu5l5GYDd2d9AP6+WZf82A7ij/ijXzofQv19CsQXAJ5j5rQBeBnB99vx6AC9nzz+RuRtlbgfwFWb+KQAXo59HY19viGgCwG8BWMnMFwKYh/7lVONbb5i5df8AXA5gl/b3zQBubjpeDefJlwD8IoCnAZybPTsXwNPZ708D2KC5n3M3iv/Qv1Z0N4A1AB4AQOif4Jxv1iH0LyK6PPs9P3NHTaehonx5PYDvmOmTesMAMAHgefTvM5+f1Zu141xvWrkCwMmCUhzKno0l2dLzZwA8BuAcZn4he/UigHOy3+OWZ38E4CMAfpz9/QYAP+D+7XPAYPrn8iZ7/0rmfhRZAuB7AD6TicfuIqLTIfUGzDwL4A8BPAfgBfTrwT6Mcb1p6wAgZBDRTwD4cwC/zcz/oL/j/tRk7PR4iejdAI4ws9zwPcx8AO8AcAcz/wz6trQG9tDGuN6cCeAa9AfJRQBOB3BVo5FqmLYOALMAztf+Pi97NlYQ0Snod/5/xsxfzB5/l4jOzd6fC+BI9nyc8uxnAfwSET2L/p3Ua9CXe59BROqaUz39c3mTvX89gO/XGeEaOQTgEDM/lv39BfQHBKk3wC8A+A4zf4+ZXwXwRfTr0tjWm7YOAHsALMt2509Ff6NmZ8NxqhUiIgB3A3iKmW/TXu0EsCn7vQn9vQH1/H2ZVsdlAF7RlvwjBTPfzMznMfNi9OvGg8z8XgBfA/CezJmZNyrP3pO5H8kZMDO/COB5Iroge3QlgAOQegP0RT+XEdHCrH2pvBnfetP0JoRnw+ZqAN8G8LcAfq/p+DSQ/p9Df5n+DQC97N/V6MsgdwN4BsBfADgrc0/oa079LYAn0Nd0aDwdNeTTagAPZL+XAngcwEEA/wvAguz5a7K/D2bvlzYd7xzoVQkAAABfSURBVIrzZBLA3qzu3A/gTKk3c3nznwF8C8CTAP4ngAXjXG/EFIQgCMKY0lYRkCAIglAxMgAIgiCMKTIACIIgjCkyAAiCIIwpMgAIgiCMKTIACIIgjCkyAAiCIIwp/x+DwjcT8Oje3gAAAABJRU5ErkJggg==\\n\",\n      \"text/plain\": [\n       \"<Figure size 432x288 with 1 Axes>\"\n      ]\n     },\n     \"metadata\": {\n      \"needs_background\": \"light\"\n     },\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"plt.imshow(Y, aspect='auto')\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Collaborative filtering learning algorithm\\n\",\n    \"\\n\",\n    \"**Exercise**: Implement collaborative filtering cost function.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 12,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def cofi_cost(params, Y, R, num_users, num_movies, num_features, _lambda):\\n\",\n    \"    \\\"\\\"\\\"\\n\",\n    \"    Collaborative filtering cost function\\n\",\n    \"    \\\"\\\"\\\"\\n\",\n    \"    \\n\",\n    \"    # unpack values\\n\",\n    \"    X = params[:num_movies*num_features].reshape((num_movies, num_features))\\n\",\n    \"    Theta = params[num_movies*num_features:].reshape((num_users, num_features))\\n\",\n    \"    \\n\",\n    \"    X_grad = np.zeros_like(X)\\n\",\n    \"    \\n\",\n    \"    return X_grad\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 13,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"def cofi_gradient(params, Y, R, num_users, num_movies, num_features, _lambda):\\n\",\n    \"    Theta = params[num_movies*num_features:].reshape((num_users, num_features))\\n\",\n    \"    Theta_grad = np.zeros_like(X)\\n\",\n    \"    \\n\",\n    \"    return Theta_grad\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"We'll load pre-trained weights to examine the cost function.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 14,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"data = sio.loadmat('ex8_movieParams.mat')\\n\",\n    \"Theta = data[\\\"Theta\\\"]\\n\",\n    \"X = data[\\\"X\\\"]\\n\",\n    \"\\n\",\n    \"# Reduce the data set size so that this runs faster\\n\",\n    \"num_users = 4\\n\",\n    \"num_movies = 5\\n\",\n    \"num_features = 3\\n\",\n    \"X_ = X[:num_movies, :num_features]\\n\",\n    \"Theta_ = Theta[:num_users, :num_features]\\n\",\n    \"Y_ = Y[:num_movies, :num_users]\\n\",\n    \"R_ = R[:num_movies, :num_users]\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"The following should return approximately $22.22$.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 15,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"'Cost at loaded parameters: 22.224603725685675'\"\n      ]\n     },\n     \"execution_count\": 15,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"J = cofi_cost(np.hstack((X_.flatten(),  Theta_.flatten())), Y_, R_, num_users, num_movies, num_features, 0)\\n\",\n    \"           \\n\",\n    \"'Cost at loaded parameters: {}'.format(J)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"The following should return approximately $31.34$.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 16,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"'Cost at loaded parameters: 31.34405624427422'\"\n      ]\n     },\n     \"execution_count\": 16,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"J = cofi_cost(np.hstack((X_.flatten(),  Theta_.flatten())), Y_, R_, num_users, num_movies, num_features, 1.5)\\n\",\n    \"           \\n\",\n    \"'Cost at loaded parameters: {}'.format(J)\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"### Training the model\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 17,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"'Toy Story (1995)\\\\n'\"\n      ]\n     },\n     \"execution_count\": 17,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"from load_movie_list import load_movie_list\\n\",\n    \"movie_list = load_movie_list()\\n\",\n    \"movie_list[0]\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 18,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"Rated 4 for Toy Story (1995)\\n\",\n      \"Rated 3 for Twelve Monkeys (1995)\\n\",\n      \"Rated 5 for Usual Suspects, The (1995)\\n\",\n      \"Rated 4 for Outbreak (1995)\\n\",\n      \"Rated 5 for Shawshank Redemption, The (1994)\\n\",\n      \"Rated 3 for While You Were Sleeping (1995)\\n\",\n      \"Rated 5 for Forrest Gump (1994)\\n\",\n      \"Rated 2 for Silence of the Lambs, The (1991)\\n\",\n      \"Rated 4 for Alien (1979)\\n\",\n      \"Rated 5 for Die Hard 2 (1990)\\n\",\n      \"Rated 5 for Sphere (1998)\\n\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"# Initialize new user ratings\\n\",\n    \"new_ratings = np.zeros((1682, 1))\\n\",\n    \"\\n\",\n    \"# Check the file movie_idx.txt for id of each movie in our dataset\\n\",\n    \"# For example, Toy Story (1995) has ID 1, so to rate it \\\"4\\\", you can set\\n\",\n    \"new_ratings[0] = 4\\n\",\n    \"\\n\",\n    \"# Or suppose did not enjoy Silence of the Lambs (1991), you can set\\n\",\n    \"new_ratings[97] = 2\\n\",\n    \"\\n\",\n    \"# We have selected a few movies we liked / did not like and the ratings we\\n\",\n    \"# gave are as follows:\\n\",\n    \"new_ratings[6] = 3\\n\",\n    \"new_ratings[11]= 5\\n\",\n    \"new_ratings[53] = 4\\n\",\n    \"new_ratings[63]= 5\\n\",\n    \"new_ratings[65]= 3\\n\",\n    \"new_ratings[68] = 5\\n\",\n    \"new_ratings[182] = 4\\n\",\n    \"new_ratings[225] = 5\\n\",\n    \"new_ratings[354]= 5\\n\",\n    \"\\n\",\n    \"for i in range(len(new_ratings)):\\n\",\n    \"    rating = new_ratings[i]\\n\",\n    \"    if rating > 0:\\n\",\n    \"        print(\\\"Rated {} for {}\\\".format(int(rating), movie_list[i]), end='')\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 19,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": [\n    \"# Add new ratings to dataset\\n\",\n    \"Y = np.hstack((new_ratings, Y))\\n\",\n    \"R = np.hstack((new_ratings != 0, R))\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 29,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"name\": \"stdout\",\n     \"output_type\": \"stream\",\n     \"text\": [\n      \"1 (1682,)\\n\",\n      \"2 (944,)\\n\",\n      \"num_users:  944  num_movies :  1682  num_features :  10\\n\",\n      \"Set initial parameters\\n\",\n      \"Train\\n\",\n      \"Warning: Desired error not necessarily achieved due to precision loss.\\n\",\n      \"         Current function value: 152936.114754\\n\",\n      \"         Iterations: 1\\n\",\n      \"         Function evaluations: 112\\n\",\n      \"         Gradient evaluations: 100\\n\",\n      \"Extract results\\n\",\n      \"[1.48354407 0.92772736 0.89064199 ... 0.34407187 0.99373252 0.53377299]\\n\",\n      \"(944,) (944,)\\n\",\n      \"Rated 11.15616688472356 for Toy Story (1995)\\n\",\n      \"Rated 11.108525219012083 for GoldenEye (1995)\\n\",\n      \"Rated 10.079762087907355 for Four Rooms (1995)\\n\",\n      \"Rated 9.851467527118134 for Get Shorty (1995)\\n\",\n      \"Rated 9.790186134596931 for Copycat (1995)\\n\",\n      \"Rated 9.643464976885834 for Shanghai Triad (Yao a yao yao dao waipo qiao) (1995)\\n\",\n      \"Rated 9.471699702534927 for Twelve Monkeys (1995)\\n\",\n      \"Rated 9.424885341163584 for Babe (1995)\\n\",\n      \"Rated 9.414902508479424 for Dead Man Walking (1995)\\n\",\n      \"Rated 9.05165410342046 for Richard III (1995)\\n\"\n     ]\n    }\n   ],\n   \"source\": [\n    \"from scipy.optimize import fmin_cg\\n\",\n    \"\\n\",\n    \"# Perform normalization\\n\",\n    \"Ymean, Ynorm = normalize_ratings(Y, R)\\n\",\n    \"\\n\",\n    \"num_users = Y.shape[1]\\n\",\n    \"num_movies = Y.shape[0]\\n\",\n    \"num_features = 10\\n\",\n    \"print('num_users: ', num_users,' num_movies : ', num_movies,' num_features : ', num_features)\\n\",\n    \"\\n\",\n    \"# Set initial parameters\\n\",\n    \"print(\\\"Set initial parameters\\\")\\n\",\n    \"X = np.random.random((num_movies, num_features))\\n\",\n    \"Theta = np.random.random((num_users, num_features))\\n\",\n    \"initial_parameters = np.hstack((X.flatten(),  Theta.flatten()))\\n\",\n    \"\\n\",\n    \"# Train\\n\",\n    \"print(\\\"Train\\\")\\n\",\n    \"_lambda = 10\\n\",\n    \"results = fmin_cg(cofi_cost, initial_parameters, args = (Y, R, num_users, num_movies, num_features, _lambda),\\n\",\n    \"                  fprime = cofi_gradient)\\n\",\n    \"\\n\",\n    \"# Extract results\\n\",\n    \"print(\\\"Extract results\\\")\\n\",\n    \"print(results)\\n\",\n    \"params = results\\n\",\n    \"X = params[:num_movies*num_features].reshape((num_movies, num_features))\\n\",\n    \"Theta = params[num_movies*num_features:].reshape((num_users, num_features))\\n\",\n    \"\\n\",\n    \"p = X @ Theta.T\\n\",\n    \"predictions = p[0, :] + Ymean\\n\",\n    \"print(predictions.shape, Ymean.shape)\\n\",\n    \"for i, prediction in enumerate(list(sorted(predictions, reverse=True))[:10]):\\n\",\n    \"    if prediction > 0:\\n\",\n    \"        print(\\\"Rated {} for {}\\\".format(prediction, movie_list[i]), end='')\"\n   ]\n  }\n ],\n \"metadata\": {\n  \"kernelspec\": {\n   \"display_name\": \"Python 3\",\n   \"language\": \"python\",\n   \"name\": \"python3\"\n  },\n  \"language_info\": {\n   \"codemirror_mode\": {\n    \"name\": \"ipython\",\n    \"version\": 3\n   },\n   \"file_extension\": \".py\",\n   \"mimetype\": \"text/x-python\",\n   \"name\": \"python\",\n   \"nbconvert_exporter\": \"python\",\n   \"pygments_lexer\": \"ipython3\",\n   \"version\": \"3.7.1\"\n  }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n"
  },
  {
    "path": "ex8/load_movie_list.py",
    "content": "def load_movie_list():\n    movies = []\n    with open('movie_ids.txt', 'r', encoding = \"ISO-8859-1\") as f:\n        for line in f.readlines():\n            movie = ' '.join(line.split(' ')[1:])\n            movies.append(movie)\n\n    return movies\n\nif __name__ == '__main__':\n    movies = load_movie_list()\n    print(movies[0])\n"
  },
  {
    "path": "ex8/movie_ids.txt",
    "content": "1 Toy Story (1995)\n2 GoldenEye (1995)\n3 Four Rooms (1995)\n4 Get Shorty (1995)\n5 Copycat (1995)\n6 Shanghai Triad (Yao a yao yao dao waipo qiao) (1995)\n7 Twelve Monkeys (1995)\n8 Babe (1995)\n9 Dead Man Walking (1995)\n10 Richard III (1995)\n11 Seven (Se7en) (1995)\n12 Usual Suspects, The (1995)\n13 Mighty Aphrodite (1995)\n14 Postino, Il (1994)\n15 Mr. Holland's Opus (1995)\n16 French Twist (Gazon maudit) (1995)\n17 From Dusk Till Dawn (1996)\n18 White Balloon, The (1995)\n19 Antonia's Line (1995)\n20 Angels and Insects (1995)\n21 Muppet Treasure Island (1996)\n22 Braveheart (1995)\n23 Taxi Driver (1976)\n24 Rumble in the Bronx (1995)\n25 Birdcage, The (1996)\n26 Brothers McMullen, The (1995)\n27 Bad Boys (1995)\n28 Apollo 13 (1995)\n29 Batman Forever (1995)\n30 Belle de jour (1967)\n31 Crimson Tide (1995)\n32 Crumb (1994)\n33 Desperado (1995)\n34 Doom Generation, The (1995)\n35 Free Willy 2: The Adventure Home (1995)\n36 Mad Love (1995)\n37 Nadja (1994)\n38 Net, The (1995)\n39 Strange Days (1995)\n40 To Wong Foo, Thanks for Everything! Julie Newmar (1995)\n41 Billy Madison (1995)\n42 Clerks (1994)\n43 Disclosure (1994)\n44 Dolores Claiborne (1994)\n45 Eat Drink Man Woman (1994)\n46 Exotica (1994)\n47 Ed Wood (1994)\n48 Hoop Dreams (1994)\n49 I.Q. (1994)\n50 Star Wars (1977)\n51 Legends of the Fall (1994)\n52 Madness of King George, The (1994)\n53 Natural Born Killers (1994)\n54 Outbreak (1995)\n55 Professional, The (1994)\n56 Pulp Fiction (1994)\n57 Priest (1994)\n58 Quiz Show (1994)\n59 Three Colors: Red (1994)\n60 Three Colors: Blue (1993)\n61 Three Colors: White (1994)\n62 Stargate (1994)\n63 Santa Clause, The (1994)\n64 Shawshank Redemption, The (1994)\n65 What's Eating Gilbert Grape (1993)\n66 While You Were Sleeping (1995)\n67 Ace Ventura: Pet Detective (1994)\n68 Crow, The (1994)\n69 Forrest Gump (1994)\n70 Four Weddings and a Funeral (1994)\n71 Lion King, The (1994)\n72 Mask, The (1994)\n73 Maverick (1994)\n74 Faster Pussycat! Kill! Kill! (1965)\n75 Brother Minister: The Assassination of Malcolm X (1994)\n76 Carlito's Way (1993)\n77 Firm, The (1993)\n78 Free Willy (1993)\n79 Fugitive, The (1993)\n80 Hot Shots! Part Deux (1993)\n81 Hudsucker Proxy, The (1994)\n82 Jurassic Park (1993)\n83 Much Ado About Nothing (1993)\n84 Robert A. Heinlein's The Puppet Masters (1994)\n85 Ref, The (1994)\n86 Remains of the Day, The (1993)\n87 Searching for Bobby Fischer (1993)\n88 Sleepless in Seattle (1993)\n89 Blade Runner (1982)\n90 So I Married an Axe Murderer (1993)\n91 Nightmare Before Christmas, The (1993)\n92 True Romance (1993)\n93 Welcome to the Dollhouse (1995)\n94 Home Alone (1990)\n95 Aladdin (1992)\n96 Terminator 2: Judgment Day (1991)\n97 Dances with Wolves (1990)\n98 Silence of the Lambs, The (1991)\n99 Snow White and the Seven Dwarfs (1937)\n100 Fargo (1996)\n101 Heavy Metal (1981)\n102 Aristocats, The (1970)\n103 All Dogs Go to Heaven 2 (1996)\n104 Theodore Rex (1995)\n105 Sgt. Bilko (1996)\n106 Diabolique (1996)\n107 Moll Flanders (1996)\n108 Kids in the Hall: Brain Candy (1996)\n109 Mystery Science Theater 3000: The Movie (1996)\n110 Operation Dumbo Drop (1995)\n111 Truth About Cats & Dogs, The (1996)\n112 Flipper (1996)\n113 Horseman on the Roof, The (Hussard sur le toit, Le) (1995)\n114 Wallace & Gromit: The Best of Aardman Animation (1996)\n115 Haunted World of Edward D. Wood Jr., The (1995)\n116 Cold Comfort Farm (1995)\n117 Rock, The (1996)\n118 Twister (1996)\n119 Maya Lin: A Strong Clear Vision (1994)\n120 Striptease (1996)\n121 Independence Day (ID4) (1996)\n122 Cable Guy, The (1996)\n123 Frighteners, The (1996)\n124 Lone Star (1996)\n125 Phenomenon (1996)\n126 Spitfire Grill, The (1996)\n127 Godfather, The (1972)\n128 Supercop (1992)\n129 Bound (1996)\n130 Kansas City (1996)\n131 Breakfast at Tiffany's (1961)\n132 Wizard of Oz, The (1939)\n133 Gone with the Wind (1939)\n134 Citizen Kane (1941)\n135 2001: A Space Odyssey (1968)\n136 Mr. Smith Goes to Washington (1939)\n137 Big Night (1996)\n138 D3: The Mighty Ducks (1996)\n139 Love Bug, The (1969)\n140 Homeward Bound: The Incredible Journey (1993)\n141 20,000 Leagues Under the Sea (1954)\n142 Bedknobs and Broomsticks (1971)\n143 Sound of Music, The (1965)\n144 Die Hard (1988)\n145 Lawnmower Man, The (1992)\n146 Unhook the Stars (1996)\n147 Long Kiss Goodnight, The (1996)\n148 Ghost and the Darkness, The (1996)\n149 Jude (1996)\n150 Swingers (1996)\n151 Willy Wonka and the Chocolate Factory (1971)\n152 Sleeper (1973)\n153 Fish Called Wanda, A (1988)\n154 Monty Python's Life of Brian (1979)\n155 Dirty Dancing (1987)\n156 Reservoir Dogs (1992)\n157 Platoon (1986)\n158 Weekend at Bernie's (1989)\n159 Basic Instinct (1992)\n160 Glengarry Glen Ross (1992)\n161 Top Gun (1986)\n162 On Golden Pond (1981)\n163 Return of the Pink Panther, The (1974)\n164 Abyss, The (1989)\n165 Jean de Florette (1986)\n166 Manon of the Spring (Manon des sources) (1986)\n167 Private Benjamin (1980)\n168 Monty Python and the Holy Grail (1974)\n169 Wrong Trousers, The (1993)\n170 Cinema Paradiso (1988)\n171 Delicatessen (1991)\n172 Empire Strikes Back, The (1980)\n173 Princess Bride, The (1987)\n174 Raiders of the Lost Ark (1981)\n175 Brazil (1985)\n176 Aliens (1986)\n177 Good, The Bad and The Ugly, The (1966)\n178 12 Angry Men (1957)\n179 Clockwork Orange, A (1971)\n180 Apocalypse Now (1979)\n181 Return of the Jedi (1983)\n182 GoodFellas (1990)\n183 Alien (1979)\n184 Army of Darkness (1993)\n185 Psycho (1960)\n186 Blues Brothers, The (1980)\n187 Godfather: Part II, The (1974)\n188 Full Metal Jacket (1987)\n189 Grand Day Out, A (1992)\n190 Henry V (1989)\n191 Amadeus (1984)\n192 Raging Bull (1980)\n193 Right Stuff, The (1983)\n194 Sting, The (1973)\n195 Terminator, The (1984)\n196 Dead Poets Society (1989)\n197 Graduate, The (1967)\n198 Nikita (La Femme Nikita) (1990)\n199 Bridge on the River Kwai, The (1957)\n200 Shining, The (1980)\n201 Evil Dead II (1987)\n202 Groundhog Day (1993)\n203 Unforgiven (1992)\n204 Back to the Future (1985)\n205 Patton (1970)\n206 Akira (1988)\n207 Cyrano de Bergerac (1990)\n208 Young Frankenstein (1974)\n209 This Is Spinal Tap (1984)\n210 Indiana Jones and the Last Crusade (1989)\n211 M*A*S*H (1970)\n212 Unbearable Lightness of Being, The (1988)\n213 Room with a View, A (1986)\n214 Pink Floyd - The Wall (1982)\n215 Field of Dreams (1989)\n216 When Harry Met Sally... (1989)\n217 Bram Stoker's Dracula (1992)\n218 Cape Fear (1991)\n219 Nightmare on Elm Street, A (1984)\n220 Mirror Has Two Faces, The (1996)\n221 Breaking the Waves (1996)\n222 Star Trek: First Contact (1996)\n223 Sling Blade (1996)\n224 Ridicule (1996)\n225 101 Dalmatians (1996)\n226 Die Hard 2 (1990)\n227 Star Trek VI: The Undiscovered Country (1991)\n228 Star Trek: The Wrath of Khan (1982)\n229 Star Trek III: The Search for Spock (1984)\n230 Star Trek IV: The Voyage Home (1986)\n231 Batman Returns (1992)\n232 Young Guns (1988)\n233 Under Siege (1992)\n234 Jaws (1975)\n235 Mars Attacks! (1996)\n236 Citizen Ruth (1996)\n237 Jerry Maguire (1996)\n238 Raising Arizona (1987)\n239 Sneakers (1992)\n240 Beavis and Butt-head Do America (1996)\n241 Last of the Mohicans, The (1992)\n242 Kolya (1996)\n243 Jungle2Jungle (1997)\n244 Smilla's Sense of Snow (1997)\n245 Devil's Own, The (1997)\n246 Chasing Amy (1997)\n247 Turbo: A Power Rangers Movie (1997)\n248 Grosse Pointe Blank (1997)\n249 Austin Powers: International Man of Mystery (1997)\n250 Fifth Element, The (1997)\n251 Shall We Dance? (1996)\n252 Lost World: Jurassic Park, The (1997)\n253 Pillow Book, The (1995)\n254 Batman & Robin (1997)\n255 My Best Friend's Wedding (1997)\n256 When the Cats Away (Chacun cherche son chat) (1996)\n257 Men in Black (1997)\n258 Contact (1997)\n259 George of the Jungle (1997)\n260 Event Horizon (1997)\n261 Air Bud (1997)\n262 In the Company of Men (1997)\n263 Steel (1997)\n264 Mimic (1997)\n265 Hunt for Red October, The (1990)\n266 Kull the Conqueror (1997)\n267 unknown\n268 Chasing Amy (1997)\n269 Full Monty, The (1997)\n270 Gattaca (1997)\n271 Starship Troopers (1997)\n272 Good Will Hunting (1997)\n273 Heat (1995)\n274 Sabrina (1995)\n275 Sense and Sensibility (1995)\n276 Leaving Las Vegas (1995)\n277 Restoration (1995)\n278 Bed of Roses (1996)\n279 Once Upon a Time... When We Were Colored (1995)\n280 Up Close and Personal (1996)\n281 River Wild, The (1994)\n282 Time to Kill, A (1996)\n283 Emma (1996)\n284 Tin Cup (1996)\n285 Secrets & Lies (1996)\n286 English Patient, The (1996)\n287 Marvin's Room (1996)\n288 Scream (1996)\n289 Evita (1996)\n290 Fierce Creatures (1997)\n291 Absolute Power (1997)\n292 Rosewood (1997)\n293 Donnie Brasco (1997)\n294 Liar Liar (1997)\n295 Breakdown (1997)\n296 Promesse, La (1996)\n297 Ulee's Gold (1997)\n298 Face/Off (1997)\n299 Hoodlum (1997)\n300 Air Force One (1997)\n301 In & Out (1997)\n302 L.A. Confidential (1997)\n303 Ulee's Gold (1997)\n304 Fly Away Home (1996)\n305 Ice Storm, The (1997)\n306 Mrs. Brown (Her Majesty, Mrs. Brown) (1997)\n307 Devil's Advocate, The (1997)\n308 FairyTale: A True Story (1997)\n309 Deceiver (1997)\n310 Rainmaker, The (1997)\n311 Wings of the Dove, The (1997)\n312 Midnight in the Garden of Good and Evil (1997)\n313 Titanic (1997)\n314 3 Ninjas: High Noon At Mega Mountain (1998)\n315 Apt Pupil (1998)\n316 As Good As It Gets (1997)\n317 In the Name of the Father (1993)\n318 Schindler's List (1993)\n319 Everyone Says I Love You (1996)\n320 Paradise Lost: The Child Murders at Robin Hood Hills (1996)\n321 Mother (1996)\n322 Murder at 1600 (1997)\n323 Dante's Peak (1997)\n324 Lost Highway (1997)\n325 Crash (1996)\n326 G.I. Jane (1997)\n327 Cop Land (1997)\n328 Conspiracy Theory (1997)\n329 Desperate Measures (1998)\n330 187 (1997)\n331 Edge, The (1997)\n332 Kiss the Girls (1997)\n333 Game, The (1997)\n334 U Turn (1997)\n335 How to Be a Player (1997)\n336 Playing God (1997)\n337 House of Yes, The (1997)\n338 Bean (1997)\n339 Mad City (1997)\n340 Boogie Nights (1997)\n341 Critical Care (1997)\n342 Man Who Knew Too Little, The (1997)\n343 Alien: Resurrection (1997)\n344 Apostle, The (1997)\n345 Deconstructing Harry (1997)\n346 Jackie Brown (1997)\n347 Wag the Dog (1997)\n348 Desperate Measures (1998)\n349 Hard Rain (1998)\n350 Fallen (1998)\n351 Prophecy II, The (1998)\n352 Spice World (1997)\n353 Deep Rising (1998)\n354 Wedding Singer, The (1998)\n355 Sphere (1998)\n356 Client, The (1994)\n357 One Flew Over the Cuckoo's Nest (1975)\n358 Spawn (1997)\n359 Assignment, The (1997)\n360 Wonderland (1997)\n361 Incognito (1997)\n362 Blues Brothers 2000 (1998)\n363 Sudden Death (1995)\n364 Ace Ventura: When Nature Calls (1995)\n365 Powder (1995)\n366 Dangerous Minds (1995)\n367 Clueless (1995)\n368 Bio-Dome (1996)\n369 Black Sheep (1996)\n370 Mary Reilly (1996)\n371 Bridges of Madison County, The (1995)\n372 Jeffrey (1995)\n373 Judge Dredd (1995)\n374 Mighty Morphin Power Rangers: The Movie (1995)\n375 Showgirls (1995)\n376 Houseguest (1994)\n377 Heavyweights (1994)\n378 Miracle on 34th Street (1994)\n379 Tales From the Crypt Presents: Demon Knight (1995)\n380 Star Trek: Generations (1994)\n381 Muriel's Wedding (1994)\n382 Adventures of Priscilla, Queen of the Desert, The (1994)\n383 Flintstones, The (1994)\n384 Naked Gun 33 1/3: The Final Insult (1994)\n385 True Lies (1994)\n386 Addams Family Values (1993)\n387 Age of Innocence, The (1993)\n388 Beverly Hills Cop III (1994)\n389 Black Beauty (1994)\n390 Fear of a Black Hat (1993)\n391 Last Action Hero (1993)\n392 Man Without a Face, The (1993)\n393 Mrs. Doubtfire (1993)\n394 Radioland Murders (1994)\n395 Robin Hood: Men in Tights (1993)\n396 Serial Mom (1994)\n397 Striking Distance (1993)\n398 Super Mario Bros. (1993)\n399 Three Musketeers, The (1993)\n400 Little Rascals, The (1994)\n401 Brady Bunch Movie, The (1995)\n402 Ghost (1990)\n403 Batman (1989)\n404 Pinocchio (1940)\n405 Mission: Impossible (1996)\n406 Thinner (1996)\n407 Spy Hard (1996)\n408 Close Shave, A (1995)\n409 Jack (1996)\n410 Kingpin (1996)\n411 Nutty Professor, The (1996)\n412 Very Brady Sequel, A (1996)\n413 Tales from the Crypt Presents: Bordello of Blood (1996)\n414 My Favorite Year (1982)\n415 Apple Dumpling Gang, The (1975)\n416 Old Yeller (1957)\n417 Parent Trap, The (1961)\n418 Cinderella (1950)\n419 Mary Poppins (1964)\n420 Alice in Wonderland (1951)\n421 William Shakespeare's Romeo and Juliet (1996)\n422 Aladdin and the King of Thieves (1996)\n423 E.T. the Extra-Terrestrial (1982)\n424 Children of the Corn: The Gathering (1996)\n425 Bob Roberts (1992)\n426 Transformers: The Movie, The (1986)\n427 To Kill a Mockingbird (1962)\n428 Harold and Maude (1971)\n429 Day the Earth Stood Still, The (1951)\n430 Duck Soup (1933)\n431 Highlander (1986)\n432 Fantasia (1940)\n433 Heathers (1989)\n434 Forbidden Planet (1956)\n435 Butch Cassidy and the Sundance Kid (1969)\n436 American Werewolf in London, An (1981)\n437 Amityville 1992: It's About Time (1992)\n438 Amityville 3-D (1983)\n439 Amityville: A New Generation (1993)\n440 Amityville II: The Possession (1982)\n441 Amityville Horror, The (1979)\n442 Amityville Curse, The (1990)\n443 Birds, The (1963)\n444 Blob, The (1958)\n445 Body Snatcher, The (1945)\n446 Burnt Offerings (1976)\n447 Carrie (1976)\n448 Omen, The (1976)\n449 Star Trek: The Motion Picture (1979)\n450 Star Trek V: The Final Frontier (1989)\n451 Grease (1978)\n452 Jaws 2 (1978)\n453 Jaws 3-D (1983)\n454 Bastard Out of Carolina (1996)\n455 Jackie Chan's First Strike (1996)\n456 Beverly Hills Ninja (1997)\n457 Free Willy 3: The Rescue (1997)\n458 Nixon (1995)\n459 Cry, the Beloved Country (1995)\n460 Crossing Guard, The (1995)\n461 Smoke (1995)\n462 Like Water For Chocolate (Como agua para chocolate) (1992)\n463 Secret of Roan Inish, The (1994)\n464 Vanya on 42nd Street (1994)\n465 Jungle Book, The (1994)\n466 Red Rock West (1992)\n467 Bronx Tale, A (1993)\n468 Rudy (1993)\n469 Short Cuts (1993)\n470 Tombstone (1993)\n471 Courage Under Fire (1996)\n472 Dragonheart (1996)\n473 James and the Giant Peach (1996)\n474 Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb (1963)\n475 Trainspotting (1996)\n476 First Wives Club, The (1996)\n477 Matilda (1996)\n478 Philadelphia Story, The (1940)\n479 Vertigo (1958)\n480 North by Northwest (1959)\n481 Apartment, The (1960)\n482 Some Like It Hot (1959)\n483 Casablanca (1942)\n484 Maltese Falcon, The (1941)\n485 My Fair Lady (1964)\n486 Sabrina (1954)\n487 Roman Holiday (1953)\n488 Sunset Blvd. (1950)\n489 Notorious (1946)\n490 To Catch a Thief (1955)\n491 Adventures of Robin Hood, The (1938)\n492 East of Eden (1955)\n493 Thin Man, The (1934)\n494 His Girl Friday (1940)\n495 Around the World in 80 Days (1956)\n496 It's a Wonderful Life (1946)\n497 Bringing Up Baby (1938)\n498 African Queen, The (1951)\n499 Cat on a Hot Tin Roof (1958)\n500 Fly Away Home (1996)\n501 Dumbo (1941)\n502 Bananas (1971)\n503 Candidate, The (1972)\n504 Bonnie and Clyde (1967)\n505 Dial M for Murder (1954)\n506 Rebel Without a Cause (1955)\n507 Streetcar Named Desire, A (1951)\n508 People vs. Larry Flynt, The (1996)\n509 My Left Foot (1989)\n510 Magnificent Seven, The (1954)\n511 Lawrence of Arabia (1962)\n512 Wings of Desire (1987)\n513 Third Man, The (1949)\n514 Annie Hall (1977)\n515 Boot, Das (1981)\n516 Local Hero (1983)\n517 Manhattan (1979)\n518 Miller's Crossing (1990)\n519 Treasure of the Sierra Madre, The (1948)\n520 Great Escape, The (1963)\n521 Deer Hunter, The (1978)\n522 Down by Law (1986)\n523 Cool Hand Luke (1967)\n524 Great Dictator, The (1940)\n525 Big Sleep, The (1946)\n526 Ben-Hur (1959)\n527 Gandhi (1982)\n528 Killing Fields, The (1984)\n529 My Life as a Dog (Mitt liv som hund) (1985)\n530 Man Who Would Be King, The (1975)\n531 Shine (1996)\n532 Kama Sutra: A Tale of Love (1996)\n533 Daytrippers, The (1996)\n534 Traveller (1997)\n535 Addicted to Love (1997)\n536 Ponette (1996)\n537 My Own Private Idaho (1991)\n538 Anastasia (1997)\n539 Mouse Hunt (1997)\n540 Money Train (1995)\n541 Mortal Kombat (1995)\n542 Pocahontas (1995)\n543 Misrables, Les (1995)\n544 Things to Do in Denver when You're Dead (1995)\n545 Vampire in Brooklyn (1995)\n546 Broken Arrow (1996)\n547 Young Poisoner's Handbook, The (1995)\n548 NeverEnding Story III, The (1994)\n549 Rob Roy (1995)\n550 Die Hard: With a Vengeance (1995)\n551 Lord of Illusions (1995)\n552 Species (1995)\n553 Walk in the Clouds, A (1995)\n554 Waterworld (1995)\n555 White Man's Burden (1995)\n556 Wild Bill (1995)\n557 Farinelli: il castrato (1994)\n558 Heavenly Creatures (1994)\n559 Interview with the Vampire (1994)\n560 Kid in King Arthur's Court, A (1995)\n561 Mary Shelley's Frankenstein (1994)\n562 Quick and the Dead, The (1995)\n563 Stephen King's The Langoliers (1995)\n564 Tales from the Hood (1995)\n565 Village of the Damned (1995)\n566 Clear and Present Danger (1994)\n567 Wes Craven's New Nightmare (1994)\n568 Speed (1994)\n569 Wolf (1994)\n570 Wyatt Earp (1994)\n571 Another Stakeout (1993)\n572 Blown Away (1994)\n573 Body Snatchers (1993)\n574 Boxing Helena (1993)\n575 City Slickers II: The Legend of Curly's Gold (1994)\n576 Cliffhanger (1993)\n577 Coneheads (1993)\n578 Demolition Man (1993)\n579 Fatal Instinct (1993)\n580 Englishman Who Went Up a Hill, But Came Down a Mountain, The (1995)\n581 Kalifornia (1993)\n582 Piano, The (1993)\n583 Romeo Is Bleeding (1993)\n584 Secret Garden, The (1993)\n585 Son in Law (1993)\n586 Terminal Velocity (1994)\n587 Hour of the Pig, The (1993)\n588 Beauty and the Beast (1991)\n589 Wild Bunch, The (1969)\n590 Hellraiser: Bloodline (1996)\n591 Primal Fear (1996)\n592 True Crime (1995)\n593 Stalingrad (1993)\n594 Heavy (1995)\n595 Fan, The (1996)\n596 Hunchback of Notre Dame, The (1996)\n597 Eraser (1996)\n598 Big Squeeze, The (1996)\n599 Police Story 4: Project S (Chao ji ji hua) (1993)\n600 Daniel Defoe's Robinson Crusoe (1996)\n601 For Whom the Bell Tolls (1943)\n602 American in Paris, An (1951)\n603 Rear Window (1954)\n604 It Happened One Night (1934)\n605 Meet Me in St. Louis (1944)\n606 All About Eve (1950)\n607 Rebecca (1940)\n608 Spellbound (1945)\n609 Father of the Bride (1950)\n610 Gigi (1958)\n611 Laura (1944)\n612 Lost Horizon (1937)\n613 My Man Godfrey (1936)\n614 Giant (1956)\n615 39 Steps, The (1935)\n616 Night of the Living Dead (1968)\n617 Blue Angel, The (Blaue Engel, Der) (1930)\n618 Picnic (1955)\n619 Extreme Measures (1996)\n620 Chamber, The (1996)\n621 Davy Crockett, King of the Wild Frontier (1955)\n622 Swiss Family Robinson (1960)\n623 Angels in the Outfield (1994)\n624 Three Caballeros, The (1945)\n625 Sword in the Stone, The (1963)\n626 So Dear to My Heart (1949)\n627 Robin Hood: Prince of Thieves (1991)\n628 Sleepers (1996)\n629 Victor/Victoria (1982)\n630 Great Race, The (1965)\n631 Crying Game, The (1992)\n632 Sophie's Choice (1982)\n633 Christmas Carol, A (1938)\n634 Microcosmos: Le peuple de l'herbe (1996)\n635 Fog, The (1980)\n636 Escape from New York (1981)\n637 Howling, The (1981)\n638 Return of Martin Guerre, The (Retour de Martin Guerre, Le) (1982)\n639 Tin Drum, The (Blechtrommel, Die) (1979)\n640 Cook the Thief His Wife & Her Lover, The (1989)\n641 Paths of Glory (1957)\n642 Grifters, The (1990)\n643 The Innocent (1994)\n644 Thin Blue Line, The (1988)\n645 Paris Is Burning (1990)\n646 Once Upon a Time in the West (1969)\n647 Ran (1985)\n648 Quiet Man, The (1952)\n649 Once Upon a Time in America (1984)\n650 Seventh Seal, The (Sjunde inseglet, Det) (1957)\n651 Glory (1989)\n652 Rosencrantz and Guildenstern Are Dead (1990)\n653 Touch of Evil (1958)\n654 Chinatown (1974)\n655 Stand by Me (1986)\n656 M (1931)\n657 Manchurian Candidate, The (1962)\n658 Pump Up the Volume (1990)\n659 Arsenic and Old Lace (1944)\n660 Fried Green Tomatoes (1991)\n661 High Noon (1952)\n662 Somewhere in Time (1980)\n663 Being There (1979)\n664 Paris, Texas (1984)\n665 Alien 3 (1992)\n666 Blood For Dracula (Andy Warhol's Dracula) (1974)\n667 Audrey Rose (1977)\n668 Blood Beach (1981)\n669 Body Parts (1991)\n670 Body Snatchers (1993)\n671 Bride of Frankenstein (1935)\n672 Candyman (1992)\n673 Cape Fear (1962)\n674 Cat People (1982)\n675 Nosferatu (Nosferatu, eine Symphonie des Grauens) (1922)\n676 Crucible, The (1996)\n677 Fire on the Mountain (1996)\n678 Volcano (1997)\n679 Conan the Barbarian (1981)\n680 Kull the Conqueror (1997)\n681 Wishmaster (1997)\n682 I Know What You Did Last Summer (1997)\n683 Rocket Man (1997)\n684 In the Line of Fire (1993)\n685 Executive Decision (1996)\n686 Perfect World, A (1993)\n687 McHale's Navy (1997)\n688 Leave It to Beaver (1997)\n689 Jackal, The (1997)\n690 Seven Years in Tibet (1997)\n691 Dark City (1998)\n692 American President, The (1995)\n693 Casino (1995)\n694 Persuasion (1995)\n695 Kicking and Screaming (1995)\n696 City Hall (1996)\n697 Basketball Diaries, The (1995)\n698 Browning Version, The (1994)\n699 Little Women (1994)\n700 Miami Rhapsody (1995)\n701 Wonderful, Horrible Life of Leni Riefenstahl, The (1993)\n702 Barcelona (1994)\n703 Widows' Peak (1994)\n704 House of the Spirits, The (1993)\n705 Singin' in the Rain (1952)\n706 Bad Moon (1996)\n707 Enchanted April (1991)\n708 Sex, Lies, and Videotape (1989)\n709 Strictly Ballroom (1992)\n710 Better Off Dead... (1985)\n711 Substance of Fire, The (1996)\n712 Tin Men (1987)\n713 Othello (1995)\n714 Carrington (1995)\n715 To Die For (1995)\n716 Home for the Holidays (1995)\n717 Juror, The (1996)\n718 In the Bleak Midwinter (1995)\n719 Canadian Bacon (1994)\n720 First Knight (1995)\n721 Mallrats (1995)\n722 Nine Months (1995)\n723 Boys on the Side (1995)\n724 Circle of Friends (1995)\n725 Exit to Eden (1994)\n726 Fluke (1995)\n727 Immortal Beloved (1994)\n728 Junior (1994)\n729 Nell (1994)\n730 Queen Margot (Reine Margot, La) (1994)\n731 Corrina, Corrina (1994)\n732 Dave (1993)\n733 Go Fish (1994)\n734 Made in America (1993)\n735 Philadelphia (1993)\n736 Shadowlands (1993)\n737 Sirens (1994)\n738 Threesome (1994)\n739 Pretty Woman (1990)\n740 Jane Eyre (1996)\n741 Last Supper, The (1995)\n742 Ransom (1996)\n743 Crow: City of Angels, The (1996)\n744 Michael Collins (1996)\n745 Ruling Class, The (1972)\n746 Real Genius (1985)\n747 Benny & Joon (1993)\n748 Saint, The (1997)\n749 MatchMaker, The (1997)\n750 Amistad (1997)\n751 Tomorrow Never Dies (1997)\n752 Replacement Killers, The (1998)\n753 Burnt By the Sun (1994)\n754 Red Corner (1997)\n755 Jumanji (1995)\n756 Father of the Bride Part II (1995)\n757 Across the Sea of Time (1995)\n758 Lawnmower Man 2: Beyond Cyberspace (1996)\n759 Fair Game (1995)\n760 Screamers (1995)\n761 Nick of Time (1995)\n762 Beautiful Girls (1996)\n763 Happy Gilmore (1996)\n764 If Lucy Fell (1996)\n765 Boomerang (1992)\n766 Man of the Year (1995)\n767 Addiction, The (1995)\n768 Casper (1995)\n769 Congo (1995)\n770 Devil in a Blue Dress (1995)\n771 Johnny Mnemonic (1995)\n772 Kids (1995)\n773 Mute Witness (1994)\n774 Prophecy, The (1995)\n775 Something to Talk About (1995)\n776 Three Wishes (1995)\n777 Castle Freak (1995)\n778 Don Juan DeMarco (1995)\n779 Drop Zone (1994)\n780 Dumb & Dumber (1994)\n781 French Kiss (1995)\n782 Little Odessa (1994)\n783 Milk Money (1994)\n784 Beyond Bedlam (1993)\n785 Only You (1994)\n786 Perez Family, The (1995)\n787 Roommates (1995)\n788 Relative Fear (1994)\n789 Swimming with Sharks (1995)\n790 Tommy Boy (1995)\n791 Baby-Sitters Club, The (1995)\n792 Bullets Over Broadway (1994)\n793 Crooklyn (1994)\n794 It Could Happen to You (1994)\n795 Richie Rich (1994)\n796 Speechless (1994)\n797 Timecop (1994)\n798 Bad Company (1995)\n799 Boys Life (1995)\n800 In the Mouth of Madness (1995)\n801 Air Up There, The (1994)\n802 Hard Target (1993)\n803 Heaven & Earth (1993)\n804 Jimmy Hollywood (1994)\n805 Manhattan Murder Mystery (1993)\n806 Menace II Society (1993)\n807 Poetic Justice (1993)\n808 Program, The (1993)\n809 Rising Sun (1993)\n810 Shadow, The (1994)\n811 Thirty-Two Short Films About Glenn Gould (1993)\n812 Andre (1994)\n813 Celluloid Closet, The (1995)\n814 Great Day in Harlem, A (1994)\n815 One Fine Day (1996)\n816 Candyman: Farewell to the Flesh (1995)\n817 Frisk (1995)\n818 Girl 6 (1996)\n819 Eddie (1996)\n820 Space Jam (1996)\n821 Mrs. Winterbourne (1996)\n822 Faces (1968)\n823 Mulholland Falls (1996)\n824 Great White Hype, The (1996)\n825 Arrival, The (1996)\n826 Phantom, The (1996)\n827 Daylight (1996)\n828 Alaska (1996)\n829 Fled (1996)\n830 Power 98 (1995)\n831 Escape from L.A. (1996)\n832 Bogus (1996)\n833 Bulletproof (1996)\n834 Halloween: The Curse of Michael Myers (1995)\n835 Gay Divorcee, The (1934)\n836 Ninotchka (1939)\n837 Meet John Doe (1941)\n838 In the Line of Duty 2 (1987)\n839 Loch Ness (1995)\n840 Last Man Standing (1996)\n841 Glimmer Man, The (1996)\n842 Pollyanna (1960)\n843 Shaggy Dog, The (1959)\n844 Freeway (1996)\n845 That Thing You Do! (1996)\n846 To Gillian on Her 37th Birthday (1996)\n847 Looking for Richard (1996)\n848 Murder, My Sweet (1944)\n849 Days of Thunder (1990)\n850 Perfect Candidate, A (1996)\n851 Two or Three Things I Know About Her (1966)\n852 Bloody Child, The (1996)\n853 Braindead (1992)\n854 Bad Taste (1987)\n855 Diva (1981)\n856 Night on Earth (1991)\n857 Paris Was a Woman (1995)\n858 Amityville: Dollhouse (1996)\n859 April Fool's Day (1986)\n860 Believers, The (1987)\n861 Nosferatu a Venezia (1986)\n862 Jingle All the Way (1996)\n863 Garden of Finzi-Contini, The (Giardino dei Finzi-Contini, Il) (1970)\n864 My Fellow Americans (1996)\n865 Ice Storm, The (1997)\n866 Michael (1996)\n867 Whole Wide World, The (1996)\n868 Hearts and Minds (1996)\n869 Fools Rush In (1997)\n870 Touch (1997)\n871 Vegas Vacation (1997)\n872 Love Jones (1997)\n873 Picture Perfect (1997)\n874 Career Girls (1997)\n875 She's So Lovely (1997)\n876 Money Talks (1997)\n877 Excess Baggage (1997)\n878 That Darn Cat! (1997)\n879 Peacemaker, The (1997)\n880 Soul Food (1997)\n881 Money Talks (1997)\n882 Washington Square (1997)\n883 Telling Lies in America (1997)\n884 Year of the Horse (1997)\n885 Phantoms (1998)\n886 Life Less Ordinary, A (1997)\n887 Eve's Bayou (1997)\n888 One Night Stand (1997)\n889 Tango Lesson, The (1997)\n890 Mortal Kombat: Annihilation (1997)\n891 Bent (1997)\n892 Flubber (1997)\n893 For Richer or Poorer (1997)\n894 Home Alone 3 (1997)\n895 Scream 2 (1997)\n896 Sweet Hereafter, The (1997)\n897 Time Tracers (1995)\n898 Postman, The (1997)\n899 Winter Guest, The (1997)\n900 Kundun (1997)\n901 Mr. Magoo (1997)\n902 Big Lebowski, The (1998)\n903 Afterglow (1997)\n904 Ma vie en rose (My Life in Pink) (1997)\n905 Great Expectations (1998)\n906 Oscar & Lucinda (1997)\n907 Vermin (1998)\n908 Half Baked (1998)\n909 Dangerous Beauty (1998)\n910 Nil By Mouth (1997)\n911 Twilight (1998)\n912 U.S. Marshalls (1998)\n913 Love and Death on Long Island (1997)\n914 Wild Things (1998)\n915 Primary Colors (1998)\n916 Lost in Space (1998)\n917 Mercury Rising (1998)\n918 City of Angels (1998)\n919 City of Lost Children, The (1995)\n920 Two Bits (1995)\n921 Farewell My Concubine (1993)\n922 Dead Man (1995)\n923 Raise the Red Lantern (1991)\n924 White Squall (1996)\n925 Unforgettable (1996)\n926 Down Periscope (1996)\n927 Flower of My Secret, The (Flor de mi secreto, La) (1995)\n928 Craft, The (1996)\n929 Harriet the Spy (1996)\n930 Chain Reaction (1996)\n931 Island of Dr. Moreau, The (1996)\n932 First Kid (1996)\n933 Funeral, The (1996)\n934 Preacher's Wife, The (1996)\n935 Paradise Road (1997)\n936 Brassed Off (1996)\n937 Thousand Acres, A (1997)\n938 Smile Like Yours, A (1997)\n939 Murder in the First (1995)\n940 Airheads (1994)\n941 With Honors (1994)\n942 What's Love Got to Do with It (1993)\n943 Killing Zoe (1994)\n944 Renaissance Man (1994)\n945 Charade (1963)\n946 Fox and the Hound, The (1981)\n947 Big Blue, The (Grand bleu, Le) (1988)\n948 Booty Call (1997)\n949 How to Make an American Quilt (1995)\n950 Georgia (1995)\n951 Indian in the Cupboard, The (1995)\n952 Blue in the Face (1995)\n953 Unstrung Heroes (1995)\n954 Unzipped (1995)\n955 Before Sunrise (1995)\n956 Nobody's Fool (1994)\n957 Pushing Hands (1992)\n958 To Live (Huozhe) (1994)\n959 Dazed and Confused (1993)\n960 Naked (1993)\n961 Orlando (1993)\n962 Ruby in Paradise (1993)\n963 Some Folks Call It a Sling Blade (1993)\n964 Month by the Lake, A (1995)\n965 Funny Face (1957)\n966 Affair to Remember, An (1957)\n967 Little Lord Fauntleroy (1936)\n968 Inspector General, The (1949)\n969 Winnie the Pooh and the Blustery Day (1968)\n970 Hear My Song (1991)\n971 Mediterraneo (1991)\n972 Passion Fish (1992)\n973 Grateful Dead (1995)\n974 Eye for an Eye (1996)\n975 Fear (1996)\n976 Solo (1996)\n977 Substitute, The (1996)\n978 Heaven's Prisoners (1996)\n979 Trigger Effect, The (1996)\n980 Mother Night (1996)\n981 Dangerous Ground (1997)\n982 Maximum Risk (1996)\n983 Rich Man's Wife, The (1996)\n984 Shadow Conspiracy (1997)\n985 Blood & Wine (1997)\n986 Turbulence (1997)\n987 Underworld (1997)\n988 Beautician and the Beast, The (1997)\n989 Cats Don't Dance (1997)\n990 Anna Karenina (1997)\n991 Keys to Tulsa (1997)\n992 Head Above Water (1996)\n993 Hercules (1997)\n994 Last Time I Committed Suicide, The (1997)\n995 Kiss Me, Guido (1997)\n996 Big Green, The (1995)\n997 Stuart Saves His Family (1995)\n998 Cabin Boy (1994)\n999 Clean Slate (1994)\n1000 Lightning Jack (1994)\n1001 Stupids, The (1996)\n1002 Pest, The (1997)\n1003 That Darn Cat! (1997)\n1004 Geronimo: An American Legend (1993)\n1005 Double vie de Vronique, La (Double Life of Veronique, The) (1991)\n1006 Until the End of the World (Bis ans Ende der Welt) (1991)\n1007 Waiting for Guffman (1996)\n1008 I Shot Andy Warhol (1996)\n1009 Stealing Beauty (1996)\n1010 Basquiat (1996)\n1011 2 Days in the Valley (1996)\n1012 Private Parts (1997)\n1013 Anaconda (1997)\n1014 Romy and Michele's High School Reunion (1997)\n1015 Shiloh (1997)\n1016 Con Air (1997)\n1017 Trees Lounge (1996)\n1018 Tie Me Up! Tie Me Down! (1990)\n1019 Die xue shuang xiong (Killer, The) (1989)\n1020 Gaslight (1944)\n1021 8 1/2 (1963)\n1022 Fast, Cheap & Out of Control (1997)\n1023 Fathers' Day (1997)\n1024 Mrs. Dalloway (1997)\n1025 Fire Down Below (1997)\n1026 Lay of the Land, The (1997)\n1027 Shooter, The (1995)\n1028 Grumpier Old Men (1995)\n1029 Jury Duty (1995)\n1030 Beverly Hillbillies, The (1993)\n1031 Lassie (1994)\n1032 Little Big League (1994)\n1033 Homeward Bound II: Lost in San Francisco (1996)\n1034 Quest, The (1996)\n1035 Cool Runnings (1993)\n1036 Drop Dead Fred (1991)\n1037 Grease 2 (1982)\n1038 Switchback (1997)\n1039 Hamlet (1996)\n1040 Two if by Sea (1996)\n1041 Forget Paris (1995)\n1042 Just Cause (1995)\n1043 Rent-a-Kid (1995)\n1044 Paper, The (1994)\n1045 Fearless (1993)\n1046 Malice (1993)\n1047 Multiplicity (1996)\n1048 She's the One (1996)\n1049 House Arrest (1996)\n1050 Ghost and Mrs. Muir, The (1947)\n1051 Associate, The (1996)\n1052 Dracula: Dead and Loving It (1995)\n1053 Now and Then (1995)\n1054 Mr. Wrong (1996)\n1055 Simple Twist of Fate, A (1994)\n1056 Cronos (1992)\n1057 Pallbearer, The (1996)\n1058 War, The (1994)\n1059 Don't Be a Menace to South Central While Drinking Your Juice in the Hood (1996)\n1060 Adventures of Pinocchio, The (1996)\n1061 Evening Star, The (1996)\n1062 Four Days in September (1997)\n1063 Little Princess, A (1995)\n1064 Crossfire (1947)\n1065 Koyaanisqatsi (1983)\n1066 Balto (1995)\n1067 Bottle Rocket (1996)\n1068 Star Maker, The (Uomo delle stelle, L') (1995)\n1069 Amateur (1994)\n1070 Living in Oblivion (1995)\n1071 Party Girl (1995)\n1072 Pyromaniac's Love Story, A (1995)\n1073 Shallow Grave (1994)\n1074 Reality Bites (1994)\n1075 Man of No Importance, A (1994)\n1076 Pagemaster, The (1994)\n1077 Love and a .45 (1994)\n1078 Oliver & Company (1988)\n1079 Joe's Apartment (1996)\n1080 Celestial Clockwork (1994)\n1081 Curdled (1996)\n1082 Female Perversions (1996)\n1083 Albino Alligator (1996)\n1084 Anne Frank Remembered (1995)\n1085 Carried Away (1996)\n1086 It's My Party (1995)\n1087 Bloodsport 2 (1995)\n1088 Double Team (1997)\n1089 Speed 2: Cruise Control (1997)\n1090 Sliver (1993)\n1091 Pete's Dragon (1977)\n1092 Dear God (1996)\n1093 Live Nude Girls (1995)\n1094 Thin Line Between Love and Hate, A (1996)\n1095 High School High (1996)\n1096 Commandments (1997)\n1097 Hate (Haine, La) (1995)\n1098 Flirting With Disaster (1996)\n1099 Red Firecracker, Green Firecracker (1994)\n1100 What Happened Was... (1994)\n1101 Six Degrees of Separation (1993)\n1102 Two Much (1996)\n1103 Trust (1990)\n1104 C'est arriv prs de chez vous (1992)\n1105 Firestorm (1998)\n1106 Newton Boys, The (1998)\n1107 Beyond Rangoon (1995)\n1108 Feast of July (1995)\n1109 Death and the Maiden (1994)\n1110 Tank Girl (1995)\n1111 Double Happiness (1994)\n1112 Cobb (1994)\n1113 Mrs. Parker and the Vicious Circle (1994)\n1114 Faithful (1996)\n1115 Twelfth Night (1996)\n1116 Mark of Zorro, The (1940)\n1117 Surviving Picasso (1996)\n1118 Up in Smoke (1978)\n1119 Some Kind of Wonderful (1987)\n1120 I'm Not Rappaport (1996)\n1121 Umbrellas of Cherbourg, The (Parapluies de Cherbourg, Les) (1964)\n1122 They Made Me a Criminal (1939)\n1123 Last Time I Saw Paris, The (1954)\n1124 Farewell to Arms, A (1932)\n1125 Innocents, The (1961)\n1126 Old Man and the Sea, The (1958)\n1127 Truman Show, The (1998)\n1128 Heidi Fleiss: Hollywood Madam (1995) \n1129 Chungking Express (1994)\n1130 Jupiter's Wife (1994)\n1131 Safe (1995)\n1132 Feeling Minnesota (1996)\n1133 Escape to Witch Mountain (1975)\n1134 Get on the Bus (1996)\n1135 Doors, The (1991)\n1136 Ghosts of Mississippi (1996)\n1137 Beautiful Thing (1996)\n1138 Best Men (1997)\n1139 Hackers (1995)\n1140 Road to Wellville, The (1994)\n1141 War Room, The (1993)\n1142 When We Were Kings (1996)\n1143 Hard Eight (1996)\n1144 Quiet Room, The (1996)\n1145 Blue Chips (1994)\n1146 Calendar Girl (1993)\n1147 My Family (1995)\n1148 Tom & Viv (1994)\n1149 Walkabout (1971)\n1150 Last Dance (1996)\n1151 Original Gangstas (1996)\n1152 In Love and War (1996)\n1153 Backbeat (1993)\n1154 Alphaville (1965)\n1155 Rendezvous in Paris (Rendez-vous de Paris, Les) (1995)\n1156 Cyclo (1995)\n1157 Relic, The (1997)\n1158 Fille seule, La (A Single Girl) (1995)\n1159 Stalker (1979)\n1160 Love! Valour! Compassion! (1997)\n1161 Palookaville (1996)\n1162 Phat Beach (1996)\n1163 Portrait of a Lady, The (1996)\n1164 Zeus and Roxanne (1997)\n1165 Big Bully (1996)\n1166 Love & Human Remains (1993)\n1167 Sum of Us, The (1994)\n1168 Little Buddha (1993)\n1169 Fresh (1994)\n1170 Spanking the Monkey (1994)\n1171 Wild Reeds (1994)\n1172 Women, The (1939)\n1173 Bliss (1997)\n1174 Caught (1996)\n1175 Hugo Pool (1997)\n1176 Welcome To Sarajevo (1997)\n1177 Dunston Checks In (1996)\n1178 Major Payne (1994)\n1179 Man of the House (1995)\n1180 I Love Trouble (1994)\n1181 Low Down Dirty Shame, A (1994)\n1182 Cops and Robbersons (1994)\n1183 Cowboy Way, The (1994)\n1184 Endless Summer 2, The (1994)\n1185 In the Army Now (1994)\n1186 Inkwell, The (1994)\n1187 Switchblade Sisters (1975)\n1188 Young Guns II (1990)\n1189 Prefontaine (1997)\n1190 That Old Feeling (1997)\n1191 Letter From Death Row, A (1998)\n1192 Boys of St. Vincent, The (1993)\n1193 Before the Rain (Pred dozhdot) (1994)\n1194 Once Were Warriors (1994)\n1195 Strawberry and Chocolate (Fresa y chocolate) (1993)\n1196 Savage Nights (Nuits fauves, Les) (1992)\n1197 Family Thing, A (1996)\n1198 Purple Noon (1960)\n1199 Cemetery Man (Dellamorte Dellamore) (1994)\n1200 Kim (1950)\n1201 Marlene Dietrich: Shadow and Light (1996) \n1202 Maybe, Maybe Not (Bewegte Mann, Der) (1994)\n1203 Top Hat (1935)\n1204 To Be or Not to Be (1942)\n1205 Secret Agent, The (1996)\n1206 Amos & Andrew (1993)\n1207 Jade (1995)\n1208 Kiss of Death (1995)\n1209 Mixed Nuts (1994)\n1210 Virtuosity (1995)\n1211 Blue Sky (1994)\n1212 Flesh and Bone (1993)\n1213 Guilty as Sin (1993)\n1214 In the Realm of the Senses (Ai no corrida) (1976)\n1215 Barb Wire (1996)\n1216 Kissed (1996)\n1217 Assassins (1995)\n1218 Friday (1995)\n1219 Goofy Movie, A (1995)\n1220 Higher Learning (1995)\n1221 When a Man Loves a Woman (1994)\n1222 Judgment Night (1993)\n1223 King of the Hill (1993)\n1224 Scout, The (1994)\n1225 Angus (1995)\n1226 Night Falls on Manhattan (1997)\n1227 Awfully Big Adventure, An (1995)\n1228 Under Siege 2: Dark Territory (1995)\n1229 Poison Ivy II (1995)\n1230 Ready to Wear (Pret-A-Porter) (1994)\n1231 Marked for Death (1990)\n1232 Madonna: Truth or Dare (1991)\n1233 Nnette et Boni (1996)\n1234 Chairman of the Board (1998)\n1235 Big Bang Theory, The (1994)\n1236 Other Voices, Other Rooms (1997)\n1237 Twisted (1996)\n1238 Full Speed (1996)\n1239 Cutthroat Island (1995)\n1240 Ghost in the Shell (Kokaku kidotai) (1995)\n1241 Van, The (1996)\n1242 Old Lady Who Walked in the Sea, The (Vieille qui marchait dans la mer, La) (1991)\n1243 Night Flier (1997)\n1244 Metro (1997)\n1245 Gridlock'd (1997)\n1246 Bushwhacked (1995)\n1247 Bad Girls (1994)\n1248 Blink (1994)\n1249 For Love or Money (1993)\n1250 Best of the Best 3: No Turning Back (1995)\n1251 A Chef in Love (1996)\n1252 Contempt (Mpris, Le) (1963)\n1253 Tie That Binds, The (1995)\n1254 Gone Fishin' (1997)\n1255 Broken English (1996)\n1256 Designated Mourner, The (1997)\n1257 Designated Mourner, The (1997)\n1258 Trial and Error (1997)\n1259 Pie in the Sky (1995)\n1260 Total Eclipse (1995)\n1261 Run of the Country, The (1995)\n1262 Walking and Talking (1996)\n1263 Foxfire (1996)\n1264 Nothing to Lose (1994)\n1265 Star Maps (1997)\n1266 Bread and Chocolate (Pane e cioccolata) (1973)\n1267 Clockers (1995)\n1268 Bitter Moon (1992)\n1269 Love in the Afternoon (1957)\n1270 Life with Mikey (1993)\n1271 North (1994)\n1272 Talking About Sex (1994)\n1273 Color of Night (1994)\n1274 Robocop 3 (1993)\n1275 Killer (Bulletproof Heart) (1994)\n1276 Sunset Park (1996)\n1277 Set It Off (1996)\n1278 Selena (1997)\n1279 Wild America (1997)\n1280 Gang Related (1997)\n1281 Manny & Lo (1996)\n1282 Grass Harp, The (1995)\n1283 Out to Sea (1997)\n1284 Before and After (1996)\n1285 Princess Caraboo (1994)\n1286 Shall We Dance? (1937)\n1287 Ed (1996)\n1288 Denise Calls Up (1995)\n1289 Jack and Sarah (1995)\n1290 Country Life (1994)\n1291 Celtic Pride (1996)\n1292 Simple Wish, A (1997)\n1293 Star Kid (1997)\n1294 Ayn Rand: A Sense of Life (1997)\n1295 Kicked in the Head (1997)\n1296 Indian Summer (1996)\n1297 Love Affair (1994)\n1298 Band Wagon, The (1953)\n1299 Penny Serenade (1941)\n1300 'Til There Was You (1997)\n1301 Stripes (1981)\n1302 Late Bloomers (1996)\n1303 Getaway, The (1994)\n1304 New York Cop (1996)\n1305 National Lampoon's Senior Trip (1995)\n1306 Delta of Venus (1994)\n1307 Carmen Miranda: Bananas Is My Business (1994)\n1308 Babyfever (1994)\n1309 Very Natural Thing, A (1974)\n1310 Walk in the Sun, A (1945)\n1311 Waiting to Exhale (1995)\n1312 Pompatus of Love, The (1996)\n1313 Palmetto (1998)\n1314 Surviving the Game (1994)\n1315 Inventing the Abbotts (1997)\n1316 Horse Whisperer, The (1998)\n1317 Journey of August King, The (1995)\n1318 Catwalk (1995)\n1319 Neon Bible, The (1995)\n1320 Homage (1995)\n1321 Open Season (1996)\n1322 Metisse (Caf au Lait) (1993)\n1323 Wooden Man's Bride, The (Wu Kui) (1994)\n1324 Loaded (1994)\n1325 August (1996)\n1326 Boys (1996)\n1327 Captives (1994)\n1328 Of Love and Shadows (1994)\n1329 Low Life, The (1994)\n1330 An Unforgettable Summer (1994)\n1331 Last Klezmer: Leopold Kozlowski, His Life and Music, The (1995)\n1332 My Life and Times With Antonin Artaud (En compagnie d'Antonin Artaud) (1993)\n1333 Midnight Dancers (Sibak) (1994)\n1334 Somebody to Love (1994)\n1335 American Buffalo (1996)\n1336 Kazaam (1996)\n1337 Larger Than Life (1996)\n1338 Two Deaths (1995)\n1339 Stefano Quantestorie (1993)\n1340 Crude Oasis, The (1995)\n1341 Hedd Wyn (1992)\n1342 Convent, The (Convento, O) (1995)\n1343 Lotto Land (1995)\n1344 Story of Xinghua, The (1993)\n1345 Day the Sun Turned Cold, The (Tianguo niezi) (1994)\n1346 Dingo (1992)\n1347 Ballad of Narayama, The (Narayama Bushiko) (1958)\n1348 Every Other Weekend (1990)\n1349 Mille bolle blu (1993)\n1350 Crows and Sparrows (1949)\n1351 Lover's Knot (1996)\n1352 Shadow of Angels (Schatten der Engel) (1976)\n1353 1-900 (1994)\n1354 Venice/Venice (1992)\n1355 Infinity (1996)\n1356 Ed's Next Move (1996)\n1357 For the Moment (1994)\n1358 The Deadly Cure (1996)\n1359 Boys in Venice (1996)\n1360 Sexual Life of the Belgians, The (1994)\n1361 Search for One-eye Jimmy, The (1996)\n1362 American Strays (1996)\n1363 Leopard Son, The (1996)\n1364 Bird of Prey (1996)\n1365 Johnny 100 Pesos (1993)\n1366 JLG/JLG - autoportrait de dcembre (1994)\n1367 Faust (1994)\n1368 Mina Tannenbaum (1994)\n1369 Forbidden Christ, The (Cristo proibito, Il) (1950)\n1370 I Can't Sleep (J'ai pas sommeil) (1994)\n1371 Machine, The (1994)\n1372 Stranger, The (1994)\n1373 Good Morning (1971)\n1374 Falling in Love Again (1980)\n1375 Cement Garden, The (1993)\n1376 Meet Wally Sparks (1997)\n1377 Hotel de Love (1996)\n1378 Rhyme & Reason (1997)\n1379 Love and Other Catastrophes (1996)\n1380 Hollow Reed (1996)\n1381 Losing Chase (1996)\n1382 Bonheur, Le (1965)\n1383 Second Jungle Book: Mowgli & Baloo, The (1997)\n1384 Squeeze (1996)\n1385 Roseanna's Grave (For Roseanna) (1997)\n1386 Tetsuo II: Body Hammer (1992)\n1387 Fall (1997)\n1388 Gabbeh (1996)\n1389 Mondo (1996)\n1390 Innocent Sleep, The (1995)\n1391 For Ever Mozart (1996)\n1392 Locusts, The (1997)\n1393 Stag (1997)\n1394 Swept from the Sea (1997)\n1395 Hurricane Streets (1998)\n1396 Stonewall (1995)\n1397 Of Human Bondage (1934)\n1398 Anna (1996)\n1399 Stranger in the House (1997)\n1400 Picture Bride (1995)\n1401 M. Butterfly (1993)\n1402 Ciao, Professore! (1993)\n1403 Caro Diario (Dear Diary) (1994)\n1404 Withnail and I (1987)\n1405 Boy's Life 2 (1997)\n1406 When Night Is Falling (1995)\n1407 Specialist, The (1994)\n1408 Gordy (1995)\n1409 Swan Princess, The (1994)\n1410 Harlem (1993)\n1411 Barbarella (1968)\n1412 Land Before Time III: The Time of the Great Giving (1995) (V)\n1413 Street Fighter (1994)\n1414 Coldblooded (1995)\n1415 Next Karate Kid, The (1994)\n1416 No Escape (1994)\n1417 Turning, The (1992)\n1418 Joy Luck Club, The (1993)\n1419 Highlander III: The Sorcerer (1994)\n1420 Gilligan's Island: The Movie (1998)\n1421 My Crazy Life (Mi vida loca) (1993)\n1422 Suture (1993)\n1423 Walking Dead, The (1995)\n1424 I Like It Like That (1994)\n1425 I'll Do Anything (1994)\n1426 Grace of My Heart (1996)\n1427 Drunks (1995)\n1428 SubUrbia (1997)\n1429 Sliding Doors (1998)\n1430 Ill Gotten Gains (1997)\n1431 Legal Deceit (1997)\n1432 Mighty, The (1998)\n1433 Men of Means (1998)\n1434 Shooting Fish (1997)\n1435 Steal Big, Steal Little (1995)\n1436 Mr. Jones (1993)\n1437 House Party 3 (1994)\n1438 Panther (1995)\n1439 Jason's Lyric (1994)\n1440 Above the Rim (1994)\n1441 Moonlight and Valentino (1995)\n1442 Scarlet Letter, The (1995)\n1443 8 Seconds (1994)\n1444 That Darn Cat! (1965)\n1445 Ladybird Ladybird (1994)\n1446 Bye Bye, Love (1995)\n1447 Century (1993)\n1448 My Favorite Season (1993)\n1449 Pather Panchali (1955)\n1450 Golden Earrings (1947)\n1451 Foreign Correspondent (1940)\n1452 Lady of Burlesque (1943)\n1453 Angel on My Shoulder (1946)\n1454 Angel and the Badman (1947)\n1455 Outlaw, The (1943)\n1456 Beat the Devil (1954)\n1457 Love Is All There Is (1996)\n1458 Damsel in Distress, A (1937)\n1459 Madame Butterfly (1995)\n1460 Sleepover (1995)\n1461 Here Comes Cookie (1935)\n1462 Thieves (Voleurs, Les) (1996)\n1463 Boys, Les (1997)\n1464 Stars Fell on Henrietta, The (1995)\n1465 Last Summer in the Hamptons (1995)\n1466 Margaret's Museum (1995)\n1467 Saint of Fort Washington, The (1993)\n1468 Cure, The (1995)\n1469 Tom and Huck (1995)\n1470 Gumby: The Movie (1995)\n1471 Hideaway (1995)\n1472 Visitors, The (Visiteurs, Les) (1993)\n1473 Little Princess, The (1939)\n1474 Nina Takes a Lover (1994)\n1475 Bhaji on the Beach (1993)\n1476 Raw Deal (1948)\n1477 Nightwatch (1997)\n1478 Dead Presidents (1995)\n1479 Reckless (1995)\n1480 Herbie Rides Again (1974)\n1481 S.F.W. (1994)\n1482 Gate of Heavenly Peace, The (1995)\n1483 Man in the Iron Mask, The (1998)\n1484 Jerky Boys, The (1994)\n1485 Colonel Chabert, Le (1994)\n1486 Girl in the Cadillac (1995)\n1487 Even Cowgirls Get the Blues (1993)\n1488 Germinal (1993)\n1489 Chasers (1994)\n1490 Fausto (1993)\n1491 Tough and Deadly (1995)\n1492 Window to Paris (1994)\n1493 Modern Affair, A (1995)\n1494 Mostro, Il (1994)\n1495 Flirt (1995)\n1496 Carpool (1996)\n1497 Line King: Al Hirschfeld, The (1996)\n1498 Farmer & Chase (1995)\n1499 Grosse Fatigue (1994)\n1500 Santa with Muscles (1996)\n1501 Prisoner of the Mountains (Kavkazsky Plennik) (1996)\n1502 Naked in New York (1994)\n1503 Gold Diggers: The Secret of Bear Mountain (1995)\n1504 Bewegte Mann, Der (1994)\n1505 Killer: A Journal of Murder (1995)\n1506 Nelly & Monsieur Arnaud (1995)\n1507 Three Lives and Only One Death (1996)\n1508 Babysitter, The (1995)\n1509 Getting Even with Dad (1994)\n1510 Mad Dog Time (1996)\n1511 Children of the Revolution (1996)\n1512 World of Apu, The (Apur Sansar) (1959)\n1513 Sprung (1997)\n1514 Dream With the Fishes (1997)\n1515 Wings of Courage (1995)\n1516 Wedding Gift, The (1994)\n1517 Race the Sun (1996)\n1518 Losing Isaiah (1995)\n1519 New Jersey Drive (1995)\n1520 Fear, The (1995)\n1521 Mr. Wonderful (1993)\n1522 Trial by Jury (1994)\n1523 Good Man in Africa, A (1994)\n1524 Kaspar Hauser (1993)\n1525 Object of My Affection, The (1998)\n1526 Witness (1985)\n1527 Senseless (1998)\n1528 Nowhere (1997)\n1529 Underground (1995)\n1530 Jefferson in Paris (1995)\n1531 Far From Home: The Adventures of Yellow Dog (1995)\n1532 Foreign Student (1994)\n1533 I Don't Want to Talk About It (De eso no se habla) (1993)\n1534 Twin Town (1997)\n1535 Enfer, L' (1994)\n1536 Aiqing wansui (1994)\n1537 Cosi (1996)\n1538 All Over Me (1997)\n1539 Being Human (1993)\n1540 Amazing Panda Adventure, The (1995)\n1541 Beans of Egypt, Maine, The (1994)\n1542 Scarlet Letter, The (1926)\n1543 Johns (1996)\n1544 It Takes Two (1995)\n1545 Frankie Starlight (1995)\n1546 Shadows (Cienie) (1988)\n1547 Show, The (1995)\n1548 The Courtyard (1995)\n1549 Dream Man (1995)\n1550 Destiny Turns on the Radio (1995)\n1551 Glass Shield, The (1994)\n1552 Hunted, The (1995)\n1553 Underneath, The (1995)\n1554 Safe Passage (1994)\n1555 Secret Adventures of Tom Thumb, The (1993)\n1556 Condition Red (1995)\n1557 Yankee Zulu (1994)\n1558 Aparajito (1956)\n1559 Hostile Intentions (1994)\n1560 Clean Slate (Coup de Torchon) (1981)\n1561 Tigrero: A Film That Was Never Made (1994)\n1562 Eye of Vichy, The (Oeil de Vichy, L') (1993)\n1563 Promise, The (Versprechen, Das) (1994)\n1564 To Cross the Rubicon (1991)\n1565 Daens (1992)\n1566 Man from Down Under, The (1943)\n1567 Careful (1992)\n1568 Vermont Is For Lovers (1992)\n1569 Vie est belle, La (Life is Rosey) (1987)\n1570 Quartier Mozart (1992)\n1571 Touki Bouki (Journey of the Hyena) (1973)\n1572 Wend Kuuni (God's Gift) (1982)\n1573 Spirits of the Dead (Tre passi nel delirio) (1968)\n1574 Pharaoh's Army (1995)\n1575 I, Worst of All (Yo, la peor de todas) (1990)\n1576 Hungarian Fairy Tale, A (1987)\n1577 Death in the Garden (Mort en ce jardin, La) (1956)\n1578 Collectionneuse, La (1967)\n1579 Baton Rouge (1988)\n1580 Liebelei (1933)\n1581 Woman in Question, The (1950)\n1582 T-Men (1947)\n1583 Invitation, The (Zaproszenie) (1986)\n1584 Symphonie pastorale, La (1946)\n1585 American Dream (1990)\n1586 Lashou shentan (1992)\n1587 Terror in a Texas Town (1958)\n1588 Salut cousin! (1996)\n1589 Schizopolis (1996)\n1590 To Have, or Not (1995)\n1591 Duoluo tianshi (1995)\n1592 Magic Hour, The (1998)\n1593 Death in Brunswick (1991)\n1594 Everest (1998)\n1595 Shopping (1994)\n1596 Nemesis 2: Nebula (1995)\n1597 Romper Stomper (1992)\n1598 City of Industry (1997)\n1599 Someone Else's America (1995)\n1600 Guantanamera (1994)\n1601 Office Killer (1997)\n1602 Price Above Rubies, A (1998)\n1603 Angela (1995)\n1604 He Walked by Night (1948)\n1605 Love Serenade (1996)\n1606 Deceiver (1997)\n1607 Hurricane Streets (1998)\n1608 Buddy (1997)\n1609 B*A*P*S (1997)\n1610 Truth or Consequences, N.M. (1997)\n1611 Intimate Relations (1996)\n1612 Leading Man, The (1996)\n1613 Tokyo Fist (1995)\n1614 Reluctant Debutante, The (1958)\n1615 Warriors of Virtue (1997)\n1616 Desert Winds (1995)\n1617 Hugo Pool (1997)\n1618 King of New York (1990)\n1619 All Things Fair (1996)\n1620 Sixth Man, The (1997)\n1621 Butterfly Kiss (1995)\n1622 Paris, France (1993)\n1623 Crmonie, La (1995)\n1624 Hush (1998)\n1625 Nightwatch (1997)\n1626 Nobody Loves Me (Keiner liebt mich) (1994)\n1627 Wife, The (1995)\n1628 Lamerica (1994)\n1629 Nico Icon (1995)\n1630 Silence of the Palace, The (Saimt el Qusur) (1994)\n1631 Slingshot, The (1993)\n1632 Land and Freedom (Tierra y libertad) (1995)\n1633  kldum klaka (Cold Fever) (1994)\n1634 Etz Hadomim Tafus (Under the Domin Tree) (1994)\n1635 Two Friends (1986) \n1636 Brothers in Trouble (1995)\n1637 Girls Town (1996)\n1638 Normal Life (1996)\n1639 Bitter Sugar (Azucar Amargo) (1996)\n1640 Eighth Day, The (1996)\n1641 Dadetown (1995)\n1642 Some Mother's Son (1996)\n1643 Angel Baby (1995)\n1644 Sudden Manhattan (1996)\n1645 Butcher Boy, The (1998)\n1646 Men With Guns (1997)\n1647 Hana-bi (1997)\n1648 Niagara, Niagara (1997)\n1649 Big One, The (1997)\n1650 Butcher Boy, The (1998)\n1651 Spanish Prisoner, The (1997)\n1652 Temptress Moon (Feng Yue) (1996)\n1653 Entertaining Angels: The Dorothy Day Story (1996)\n1654 Chairman of the Board (1998)\n1655 Favor, The (1994)\n1656 Little City (1998)\n1657 Target (1995)\n1658 Substance of Fire, The (1996)\n1659 Getting Away With Murder (1996)\n1660 Small Faces (1995)\n1661 New Age, The (1994)\n1662 Rough Magic (1995)\n1663 Nothing Personal (1995)\n1664 8 Heads in a Duffel Bag (1997)\n1665 Brother's Kiss, A (1997)\n1666 Ripe (1996)\n1667 Next Step, The (1995)\n1668 Wedding Bell Blues (1996)\n1669 MURDER and murder (1996)\n1670 Tainted (1998)\n1671 Further Gesture, A (1996)\n1672 Kika (1993)\n1673 Mirage (1995)\n1674 Mamma Roma (1962)\n1675 Sunchaser, The (1996)\n1676 War at Home, The (1996)\n1677 Sweet Nothing (1995)\n1678 Mat' i syn (1997)\n1679 B. Monkey (1998)\n1680 Sliding Doors (1998)\n1681 You So Crazy (1994)\n1682 Scream of Stone (Schrei aus Stein) (1991)\n"
  },
  {
    "path": "requirements.txt",
    "content": "cycler==0.10.0\nkiwisolver==1.1.0\nmatplotlib==3.1.1\nnltk==3.4.5\nnumpy==1.16.4\npandas==0.24.2\nPillow==8.1.1\npyparsing==2.4.0\npython-dateutil==2.8.0\npytz==2019.1\nscipy==1.3.0\nsix==1.12.0\n"
  },
  {
    "path": "week6/1-Evaluating-a-Learning-Algorithm.md",
    "content": "# Advice for Applying Machine Learning\n\n## Evaluating a Learning Algorithm\n\n### What to do next?\n\nIf you trained your model and the model is performing worse than you had expected you may want to try the following things:\n* Get more training data (do not spend too much time as this does not always yield better results)\n* Try smaller sets of features\n* Try getting additional features\n* Try adding polynomial features\n* Try decreasing/increasing $\\lambda$.\n\nDo not randomly pick an option from the list above. Use a **machine learning diagnostic**: a test that you can run to gain insight in what is isn't working with a learning algorithm, and gain guidance as to how best improve its performance.\n\n### Evaluating your hypothesis\n\nA low training error does not necessarily mean a good hypothesis function. To prevent overfitting, split the data into a training set and test set. Usually 70% of the data is in the training set and 30% is in the test set.\n\n### Model selection\n\n$d$: Degree of polynomial\n\nYou may want to try out multiple values for $d$, $\\lambda$, and so on. Then you choose the best values for $\\Theta$ on a set that the model has not seen before. If you did this, however, on the test set you get a too optimistic accuracy. That's the reason we want to split our data into 3 sets: the training set (60%), the cross validation set (20%), the test set (20%). You use the training set for training, the cross validation set for model selection and the test set to obtain the accuracy.\n\nThe errors: \n\nTraining error: $J_{train}(\\theta) = \\frac{1}{2m}\\displaystyle\\sum_{i = 0}^{m}(h_\\theta(x^{(i)})-y^{(i)})^2$\n\nCross validation error: $J_{cv}(\\theta) = \\frac{1}{2m_{cv}}\\displaystyle\\sum_{i = 0}^{m_{cv}}(h_\\theta(x_{cv}^{(i)})-y_{cv}^{(i)})^2$\n\nTest error: $J_{cv}(\\theta) = \\frac{1}{2m_{test}}\\displaystyle\\sum_{i = 0}^{m_{test}}(h_\\theta(x_{test}^{(i)})-y_{test}^{(i)})^2$\n\nYou want to choose the values for $d$ from $1, 2, …, 10$ and $\\lambda$ in $0.00, 0.02, 0.04, …, 10$.\n\n## Bias vs. Variance\n\nHigh bias: underfitting. High variance: overfitting.\n\n### Learning curves\n\n![learning curves](/Users/rickwierenga/Desktop/cs229/programming/week6/learning_curves.png)\n\n![high bias](high_bias.png)\n\n![high variance](high_variance.png)\n\n### Deciding what to do next\n\n- Get more training data (do not spend too much time as this does not always yield better results): fixes high variance\n- Try smaller sets of features: fixes high variance\n- Try getting additional features: fixes high bias\n- Try adding polynomial features: fixes high bias\n- Try decreasing $\\lambda$:  fixes high bias\n- increasing $\\lambda$: fixes high variance\n\nSmall neural networks are more prone to overfitting but computationally cheaper. Large neural networks are more prone to overfitting and computationally more expensive. Use $\\lambda$ to prevent overfitting.\n\n## Building a spam filter\n\n### Error analysis\n\n- Start with a simple algorithm that you can implement quickly. Implement it and test it on your cross-validation data.\n- Plot learning curves to decide if more data, more features, etc. are likely to help\n- Error analysis: Manually examine the examples (in cross validation set) that your algorithm made errors on. See if you can spot any systematic trend in what type of examples it is making errors on.\n\nUse numerical evaluation.\n\n### Handling skewed data\n\n|      | 1              | 0              |\n| ---- | -------------- | -------------- |\n| 1    | True positive  | False positive |\n| 0    | False negative | True negative  |\n\n$P = precision = \\frac{True\\ positives}{True\\ positives+False\\ positives}$\n\n$R = recall = \\frac{True\\ positives}{True\\ positives+False\\ negatives}$\n\nTrading off precision and recall: predict 1 if $h_\\theta(x) \\geqslant threshold$\n\nSingle method for rating the accuracy: $F_1 = 2\\frac{PR}{P+R}$\n\n## Using large datasets\n\nUseful test: Given the input $x$, can a human expert confidently predict $y$.\n"
  }
]