Full Code of ziatdinovmax/gpax for AI

Repository: ziatdinovmax/gpax
Branch: main
Commit: b493ba26c061
Files: 101
Total size: 23.8 MB

Directory structure:
gitextract_po1u8joa/

├── .flake8
├── .github/
│   └── workflows/
│       ├── ci-deploy.yml
│       ├── ci.yml
│       ├── notebook_smoke.yml
│       └── unit.yml
├── .gitignore
├── .readthedocs.yml
├── LICENSE
├── README.md
├── docs/
│   ├── Makefile
│   ├── make.bat
│   ├── requirements_rtd.txt
│   └── source/
│       ├── LICENSE.rst
│       ├── README.rst
│       ├── USAGE.rst
│       ├── acquisition.rst
│       ├── conf.py
│       ├── examples.rst
│       ├── hypo.rst
│       ├── index.rst
│       ├── kernels.rst
│       ├── models.rst
│       ├── priors.rst
│       └── utils.rst
├── examples/
│   ├── GP_sGP.ipynb
│   ├── GPax_MultiTaskGP_BO.ipynb
│   ├── MeasuredNoiseGP.ipynb
│   ├── compare_GPs.ipynb
│   ├── contrib/
│   │   ├── cBO_1D_GPax_tutorial.ipynb
│   │   └── gpax_dkl_notebookIII_molecules.ipynb
│   ├── gpax_GPBO.ipynb
│   ├── gpax_UIGP.ipynb
│   ├── gpax_hypo.ipynb
│   ├── gpax_simpleGP.ipynb
│   ├── gpax_simpleGP_tutorial.ipynb
│   ├── gpax_viDKL_plasmons.ipynb
│   ├── gpax_viGP.ipynb
│   ├── heteroskedasticGP.ipynb
│   └── simpleGP.ipynb
├── gpax/
│   ├── __init__.py
│   ├── _version.py
│   ├── acquisition/
│   │   ├── __init__.py
│   │   ├── acquisition.py
│   │   ├── base_acq.py
│   │   ├── batch_acquisition.py
│   │   ├── optimize.py
│   │   └── penalties.py
│   ├── hypo.py
│   ├── kernels/
│   │   ├── __init__.py
│   │   ├── kernels.py
│   │   └── mtkernels.py
│   ├── models/
│   │   ├── __init__.py
│   │   ├── bnn.py
│   │   ├── corgp.py
│   │   ├── dkl.py
│   │   ├── gp.py
│   │   ├── hskgp.py
│   │   ├── ibnn.py
│   │   ├── linreg.py
│   │   ├── mngp.py
│   │   ├── mtgp.py
│   │   ├── sparse_gp.py
│   │   ├── spm.py
│   │   ├── uigp.py
│   │   ├── vgp.py
│   │   ├── vi_ibnn.py
│   │   ├── vi_mtdkl.py
│   │   ├── vidkl.py
│   │   └── vigp.py
│   ├── priors/
│   │   ├── __init__.py
│   │   └── priors.py
│   └── utils/
│       ├── __init__.py
│       ├── fn.py
│       └── utils.py
├── pyproject.toml
├── scripts/
│   ├── build.sh
│   ├── install.sh
│   └── test_notebooks.sh
└── tests/
    ├── __init__.py
    ├── test_acq.py
    ├── test_bnn.py
    ├── test_corgp.py
    ├── test_dkl.py
    ├── test_func_setter.py
    ├── test_gp.py
    ├── test_hskgp.py
    ├── test_hypo.py
    ├── test_ibnn.py
    ├── test_kernels.py
    ├── test_mngp.py
    ├── test_mtgp.py
    ├── test_optimize_acq.py
    ├── test_priors.py
    ├── test_sparsegp.py
    ├── test_spm.py
    ├── test_uigp.py
    ├── test_utils.py
    ├── test_vgp.py
    ├── test_vidkl.py
    ├── test_vigp.py
    └── test_vimtdkl.py

================================================
FILE CONTENTS
================================================

================================================
FILE: .flake8
================================================
[flake8]
exclude =
    .git,
    __pycache__,
    build,
    dist,
    docs/source/conf.py
max-line-length = 80
show-source = True
statistics = True
count = True
verbose = 1
ignore = E203, W503


================================================
FILE: .github/workflows/ci-deploy.yml
================================================
name: CI/Deploy

on:
  push:
    tags: ["v*"]

jobs:

  unit:
    uses: ./.github/workflows/unit.yml

  notebooks:
    uses: ./.github/workflows/notebook_smoke.yml

  build_and_publish:
    name: Upload release to PyPI
    if: github.event_name == 'push' && startsWith(github.ref, 'refs/tags')
    runs-on: ubuntu-latest
    environment:
      name: pypi
      url: https://pypi.org/p/gpax
    permissions:
      id-token: write

    needs:
      - unit
      - notebooks

    steps:

    - name: Checkout
      uses: actions/checkout@v3
      with:
        fetch-depth: 0

    - name: Set up Python 3.9
      uses: actions/setup-python@v2
      with:
        python-version: 3.12

    - name: Build and apply version
      run: bash scripts/build.sh

    - name: Publish package distributions to PyPI
      uses: pypa/gh-action-pypi-publish@release/v1
      with:
        # CURRENTLY USING TEST SERVER FOR NOW!!!!
        repository-url: https://test.pypi.org/legacy/


================================================
FILE: .github/workflows/ci.yml
================================================
name: CI

on:

  pull_request:
    branches: ["main", "dev/*"]

  push:
    branches: ["main", "dev/*"]

jobs: 

  unit:
    uses: ./.github/workflows/unit.yml

  notebooks:
    uses: ./.github/workflows/notebook_smoke.yml


================================================
FILE: .github/workflows/notebook_smoke.yml
================================================
name: notebooks

env:
  CI_SMOKE: True

on:
  workflow_call:

jobs:
  build-linux:
    
    strategy:
      matrix:
        python-version: ['3.11', '3.12']
        os: [ubuntu-latest]

    runs-on: ${{ matrix.os }}

    steps:
    - uses: actions/checkout@v2
      
    - name: Set up Python ${{ matrix.python-version }}
      
      uses: actions/setup-python@v2
      with:
        python-version: ${{ matrix.python-version }}

    - name: Install dependencies
      run: |
        bash scripts/install.sh

    - name: Notebook smoke tests
      run: |
        bash scripts/test_notebooks.sh



================================================
FILE: .github/workflows/unit.yml
================================================
name: Unit
env:
  PYTHON_MAIN_VERSION: 3.12
on:
  workflow_call:
jobs:
  build:
    runs-on: ${{ matrix.os }}
    strategy:
      matrix:
        os: [ubuntu-latest]
        python-version: ["3.11", "3.12"]
    steps:
      - uses: actions/checkout@v4
      - name: Set up Python ${{ matrix.python-version }}
        uses: actions/setup-python@v4
        with:
          python-version: ${{ matrix.python-version }}
      - name: Install dependencies
        run: |
          bash scripts/install.sh
          bash scripts/install.sh test
      - name: Lint with flake8
        run: |
          # stop the build if there are Python syntax errors or undefined names
          flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics
          # exit-zero treats all errors as warnings. The GitHub editor is 127 chars wide
          flake8 . --count --exit-zero --max-complexity=10 --max-line-length=127 --statistics
      - name: Run tests
        run: |
          pytest -v --cov --cov-report=xml --cov-report=term tests
      - name: Upload coverage to Codecov
        if: ${{ matrix.python-version == env.PYTHON_MAIN_VERSION }}
        uses: codecov/codecov-action@v4
        with:
          token: ${{ secrets.CODECOV_TOKEN }}
          file: ./coverage.xml
          flags: unittests
          name: codecov-umbrella
          fail_ci_if_error: false
          verbose: true


================================================
FILE: .gitignore
================================================
# Byte-compiled / optimized / DLL files
__pycache__/
*.py[cod]
*$py.class

# C extensions
*.so

# Distribution / packaging
.Python
build/
develop-eggs/
dist/
downloads/
eggs/
.eggs/
lib/
lib64/
parts/
sdist/
var/
wheels/
pip-wheel-metadata/
share/python-wheels/
*.egg-info/
.installed.cfg
*.egg
MANIFEST

# PyInstaller
#  Usually these files are written by a python script from a template
#  before PyInstaller builds the exe, so as to inject date/other infos into it.
*.manifest
*.spec

# Installer logs
pip-log.txt
pip-delete-this-directory.txt

# Unit test / coverage reports
htmlcov/
.tox/
.nox/
.coverage
.coverage.*
.cache
nosetests.xml
coverage.xml
*.cover
*.py,cover
.hypothesis/
.pytest_cache/

# Translations
*.mo
*.pot

# Django stuff:
*.log
local_settings.py
db.sqlite3
db.sqlite3-journal

# Flask stuff:
instance/
.webassets-cache

# Scrapy stuff:
.scrapy

# Sphinx documentation
docs/_build/

# PyBuilder
target/

# Jupyter Notebook
.ipynb_checkpoints

# IPython
profile_default/
ipython_config.py

# pyenv
.python-version

# pipenv
#   According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
#   However, in case of collaboration, if having platform-specific dependencies or dependencies
#   having no cross-platform support, pipenv may install dependencies that don't work, or not
#   install all needed dependencies.
#Pipfile.lock

# PEP 582; used by e.g. github.com/David-OConnor/pyflow
__pypackages__/

# Celery stuff
celerybeat-schedule
celerybeat.pid

# SageMath parsed files
*.sage.py

# Environments
.env
.venv
env/
venv/
ENV/
env.bak/
venv.bak/

# Spyder project settings
.spyderproject
.spyproject

# Rope project settings
.ropeproject

# mkdocs documentation
/site

# mypy
.mypy_cache/
.dmypy.json
dmypy.json

# Pyre type checker
.pyre/

# Pyright
pyrightconfig.json


================================================
FILE: .readthedocs.yml
================================================
# .readthedocs.yml
# Read the Docs configuration file
# See https://docs.readthedocs.io/en/stable/config-file/v2.html for details

# Required
version: 2

build:
  os: "ubuntu-22.04"
  tools:
    python: "3.11"

# Build documentation in the docs/ directory with Sphinx
sphinx:
  configuration: docs/source/conf.py

# Build documentation with MkDocs
#mkdocs:
#  configuration: mkdocs.yml

# Optionally build your docs in additional formats such as PDF and ePub
formats: []

# Optionally set the version of Python and requirements required to build your docs
python:
  install:
    - requirements: docs/requirements_rtd.txt


================================================
FILE: LICENSE
================================================
MIT License

Copyright (c) 2024 GPax authors

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.


================================================
FILE: README.md
================================================
# GPax
[![build](https://github.com/ziatdinovmax/gpax/actions/workflows/ci.yml/badge.svg)](https://github.com/ziatdinovmax/gpax/actions/workflows/ci.yml)
[![notebooks](https://github.com/ziatdinovmax/gpax/actions/workflows/notebook_smoke.yml/badge.svg)](https://github.com/ziatdinovmax/gpax/actions/workflows/notebook_smoke.yml)
[![codecov](https://codecov.io/gh/ziatdinovmax/gpax/branch/main/graph/badge.svg?token=FFA8XB0FED)](https://codecov.io/gh/ziatdinovmax/gpax)
[![Documentation Status](https://readthedocs.org/projects/gpax/badge/?version=latest)](https://gpax.readthedocs.io/en/latest/?badge=latest)
[![PyPI version](https://badge.fury.io/py/gpax.svg)](https://badge.fury.io/py/gpax)

GPax is a small Python package for physics-based Gaussian processes (GPs) built on top of NumPyro and JAX. Its purpose is to take advantage of prior physical knowledge and different data modalities when using GPs for data reconstruction and active learning. It is a work in progress, and more models will be added in the near future.

![GPax_logo](https://github.com/ziatdinovmax/gpax/assets/34245227/f2117b9d-d64b-4e48-9b91-e5c7f220b866)

## How to use
### Simple GP
#### *1D Example*
[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/gpax_simpleGP.ipynb)

The code snippet below shows how to use vanilla GP in a fully Bayesian mode. First, we infer GP model parameters from the available training data
```python3
import gpax

# Get random number generator keys for training and prediction
rng_key, rng_key_predict = gpax.utils.get_keys()
# Initialize model
gp_model = gpax.ExactGP(1, kernel='RBF')
# Run Hamiltonian Monte Carlo to obtain posterior samples for the GP model parameters
gp_model.fit(rng_key, X, y)  # X and y are numpy arrays with dimensions (n, d) and (n,)
```
In the fully Bayesian mode, we get a pair of predictive mean and covariance for each Hamiltonian Monte Carlo sample containing the GP parameters (in this case, the RBF kernel hyperparameters and model noise). Hence, a prediction on new inputs with a trained GP model returns the center of the mass of all the predictive means (```posterior_mean```) and samples from multivariate normal distributions for all the pairs of predictive means and covariances (```f_samples```).
```python3
posterior_mean, f_samples = gp_model.predict(rng_key_predict, X_test)
```

<img src = "https://user-images.githubusercontent.com/34245227/167945293-8cb5b88a-1f64-4f7d-95ab-26863b90d1e5.jpg" height="60%" width="60%">

For 1-dimensional data, we can plot the GP prediction using the standard approach where the uncertainty in predictions - represented by a standard deviation in ```y_sampled``` - is depicted as a shaded area around the mean value.

<img src = "https://user-images.githubusercontent.com/34245227/167945487-05068084-86cb-4104-a792-d39d2f834151.jpg" height="60%" width="60%">

See the full example, including specification of custom GP kernel priors, [here](https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/gpax_simpleGP.ipynb).

#### *Sparse Image Reconstruction*
[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/gpax_viGP.ipynb)

One can also use GP for sparse image reconstruction. The fully Bayesian GP is typically too slow for this purpose and it makes sense to use a stochastic variational inference approximation (viGP) instead. Code-wise, the usage of viGP in GPax is almost the same as that of the fully Bayesian GP. One difference is that instead of ```num_samples``` we have ```num_steps```. We can also control the learning rate by specifying a ```step_size```. 
```python3
# Get training inputs/targets and full image indices from sparse image data
X_train, y_train, X_full = gpax.utils.preprocess_sparse_image(sparse_img) # sparse_img is a 2D numpy array

# Initialize and train a variational inference GP model
gp_model = gpax.viGP(2, kernel='Matern', guide='delta')
gp_model.fit(rng_key, X_train, y_train, num_steps=250, step_size=0.05)
```

When we run the ```.predict()``` method, the output is predictive mean and variance computed from a learned single estimate of the GP model parameters:
```python3
y_pred, y_var = gp_model.predict(rng_key_predict, X_full)
```
![viGP](https://github.com/ziatdinovmax/gpax/assets/34245227/ac9043be-dc91-46ea-88f4-42471308d149)

Finally, for larger images or hyperspecteral data, one can use the [inducing inputs](https://www.jmlr.org/papers/volume6/quinonero-candela05a/quinonero-candela05a.pdf) approximation to GP, which is also available in GPax. See the full example [here](https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/gpax_viGP.ipynb).

### Structured GP
[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/GP_sGP.ipynb)

The limitation of the standard GP is that it does not usually allow for the incorporation of prior domain knowledge and can be biased toward a trivial interpolative solution. Recently, we [introduced](https://arxiv.org/abs/2108.10280) a structured Gaussian Process (sGP), where a classical GP is augmented by a structured probabilistic model of the expected system’s behavior. This approach allows us to [balance](https://towardsdatascience.com/unknown-knowns-bayesian-inference-and-structured-gaussian-processes-why-domain-scientists-know-4659b7e924a4) the flexibility of the non-parametric GP approach with a rigid structure of prior (physical) knowledge encoded into the parametric model.
Implementation-wise, we substitute a constant/zero prior mean function in GP with a probabilistic model of the expected system's behavior.

For example, if we have prior knowledge that our objective function has a discontinuous 'phase transition', and a power law-like behavior before and after this transition, we may express it using a simple piecewise function
```python3
import jax.numpy as jnp

def piecewise(x: jnp.ndarray, params: Dict[str, float]) -> jnp.ndarray:
    """Power-law behavior before and after the transition"""
    return jnp.piecewise(
        x, [x < params["t"], x >= params["t"]],
        [lambda x: x**params["beta1"], lambda x: x**params["beta2"]])
```
where ```jnp``` corresponds to jax.numpy module. This function is deterministic. To make it probabilistic, we put priors over its parameters with the help of [NumPyro](https://github.com/pyro-ppl/numpyro)
```python3
import numpyro
from numpyro import distributions

def piecewise_priors():
    # Sample model parameters
    t = numpyro.sample("t", distributions.Uniform(0.5, 2.5))
    beta1 = numpyro.sample("beta1", distributions.Normal(3, 1))
    beta2 = numpyro.sample("beta2", distributions.Normal(3, 1))
    # Return sampled parameters as a dictionary
    return {"t": t, "beta1": beta1, "beta2": beta2}
```
Finally, we train the sGP model and make predictions on new data in the almost exact same way we did for vanilla GP. The only difference is that we pass our structured probabilistic model as two new arguments (the piecewise function and the corresponding priors over its parameters) when initializing GP.
```python3
# Get random number generator keys
rng_key, rng_key_predict = gpax.utils.get_keys()
# initialize structured GP model
sgp_model = gpax.ExactGP(1, kernel='Matern', mean_fn=piecewise, mean_fn_prior=piecewise_priors)
# Run MCMC to obtain posterior samples
sgp_model.fit(rng_key, X, y)
# Get GP prediction on new/test data
posterior_mean, f_samples = sgp_model.predict(rng_key_predict, X_test)
```

![GP_vs_sGP2](https://github.com/ziatdinovmax/gpax/assets/34245227/89de341c-f00c-468c-afe6-c0b1c1140725)


Structured GP is usually better at extrapolation and provides more reasonable uncertainty estimates. The probabilistic model in structured GP reflects our prior knowledge about the system, but it does not have to be precise, that is, the model can have a different functional form, as long as it captures general or partial trends in the data. The full example including the active learning part is available [here](https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/GP_sGP.ipynb).


### Active learning and Bayesian optimization
[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/gpax_GPBO.ipynb)

Both GP and sGP can be used for active learning to reconstruct the entire data distribution from sparse observations or to localize regions of the parameter space where a particular physical behavior is maximized or minimized with as few measurements as possible (the latter is usually referred to as [Bayesian optimization](https://ieeexplore.ieee.org/abstract/document/7352306)).

```python3
# Train a GP model (it can be sGP or vanilla GP)
gp_model.fit(rng_key, X_measured, y_measured)  # A

# Compute the upper confidence bound (UCB) acquisition function to derive the next measurement point
acq = gpax.acquisition.UCB(rng_key_predict, gp_model, X_unmeasured, beta=4, maximize=False, noiseless=True)  # B
next_point_idx = acq.argmax()  # C
next_point = X_unmeasured[next_point_idx]  # D

# Perform measurement in next_point, update measured & unmeasured data arrays, and re-run steps A-D.
```

In the figure below we illustrate the connection between the (s)GP posterior predictive distribution and the acquisition function used to derive the next measurement points. Here, the posterior mean values indicate that the minimum of a "black box" function describing a behavior of interest is around $x=0.7$. At the same time, there is a large dispersion in the samples from the posterior predictive distribution between $x=-0.5$ and $x=0.5$, resulting in high uncertainty in that region. The acquisition function is computed as a function of both predictive mean and uncertainty and its maximum corresponds to the next measurement point in the active learning and Bayesian optimization. Here, after taking into account the uncertainty in the prediction, the UCB acquisition function suggests exploring a point at x≈0 where potentially a true minimum is located. See full example [here](https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/gpax_GPBO.ipynb).

<img src="https://github.com/ziatdinovmax/gpax/assets/34245227/24f641fb-5959-4780-8d0e-edf62bd0a32b">


### Theory-informed data reconstruction and Bayesian optimization
[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/GPax_MultiTaskGP_BO.ipynb)

Sometimes when theoretical simulations are available before the experiment, they can be used to guide the measurements or simply reconstruct sparse data via a multi-task/fidelity Gaussian process. This can be used as an alternative solution to a structured Gaussian process in situations where a mean function is too costly to compute at each step or it is expressed through some complex program that is not fully differentiable. The overall scheme is the same, but now our GP model is a MultitaskGP:

```python3
key1, key2 = gpax.utils.get_keys(1)

gp_model = gpax.MultiTaskGP(
    input_dim=1, data_kernel='Matern',  # standard GP parameters
    shared_input_space=False,  # different tasks/fidelities have different numbers of observations
    num_latents=2, rank=2,  # parameters of multi-task GP
)

model.fit(key1, X, y, num_warmup=500, num_samples=500)
```

Note that X has (N, D+1) dimensions where the last column contains task/fidelity indices for each observation. We can then use the trained model to make a prediction for partially observed data:
```python3
# Create a set of inputs for the task/fidelity 2
X_unmeasured2 = np.column_stack((X_full_range, np.ones_like(X_full_range)))

# Make a prediction with the trained model
posterior_mean2, f_samples2  = model.predict(key2, X_unmeasured2, noiseless=True)
```

![GP_vs_MTGP](https://github.com/ziatdinovmax/gpax/assets/34245227/5a36d3cd-c904-4345-abc3-b1bea5025cc8)
The full example including Bayesian optimization is available [here](https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/GPax_MultiTaskGP_BO.ipynb)



### Hypothesis learning
[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/gpax_hypo.ipynb)

The structured GP can also be used for hypothesis learning in automated experiments. The [hypothesis learning](https://arxiv.org/abs/2112.06649) is based on the idea that in active learning, the correct model of the system’s behavior leads to a faster decrease in the overall Bayesian uncertainty about the system under study. In the hypothesis learning setup, probabilistic models of the possible system’s behaviors (hypotheses) are wrapped into structured GPs, and a basic reinforcement learning policy is used to select a correct model from several competing hypotheses. The example of hypothesis learning on toy data is available [here](https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/gpax_hypo.ipynb).

<img src="https://user-images.githubusercontent.com/34245227/167936394-52f5ffd5-a47c-425d-b8a7-0727938dfab2.gif">


### Deep kernel learning
[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/gpax_viDKL_plasmons.ipynb)

[Deep kernel learning (DKL)](https://arxiv.org/abs/1511.02222) can be understood as a hybrid of deep neural network (DNN) and GP. The DNN serves as a feature extractor that allows reducing the complex high-dimensional features to low-dimensional descriptors on which a standard GP kernel operates. The parameters of DNN and of GP kernel are inferred jointly in an end-to-end fashion. Practically, the DKL training inputs are usually patches from an (easy-to-acquire) structural image, and training targets represent a physical property of interest derived from the (hard-to-acquire) spectra measured in those patches. The DKL output on the new inputs (image patches for which there are no measured spectra) is the expected property value and associated uncertainty, which can be used to derive the next measurement point in the automated experiment. 

GPax package has the fully Bayesian DKL (weights of neural network and GP hyperparameters are inferred using Hamiltonian Monte Carlo) and the Variational Inference approximation of DKL, viDKL. The fully Bayesian DKL can provide an asymptotically exact solution but is too slow for most automated experiments. Hence, for the latter, one may use the viDKL
```python3
import gpax

# Get random number generator keys for training and prediction
rng_key, rng_key_predict = gpax.utils.get_keys()

# Obtain/update DKL posterior; input data dimensions are (n, h*w*c)
dkl = gpax.viDKL(input_dim=X.shape[-1], z_dim=2, kernel='RBF')  # A
dkl.fit(rng_key, X_train, y_train, num_steps=100, step_size=0.05)  # B

# Compute UCB acquisition function
obj = gpax.acquisition.UCB(rng_key_predict, dkl, X_unmeasured, maximize=True)  # C
# Select next point to measure (assuming grid data)
next_point_idx = obj.argmax()  # D

# Perform measurement in next_point_idx, update measured & unmeasured data arrays, and re-run steps A-D.
```
Below we show a result of a simple DKL-based search for regions of the nano-plasmonic array that [host edge plasmons](https://arxiv.org/abs/2108.03290). The full example is available [here](https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/gpax_viDKL_plasmons.ipynb). 

<img src="https://user-images.githubusercontent.com/34245227/160270568-147fa21b-91f3-48b8-8dd2-c33eb4b497b4.png">

Note that in viDKL, we use a simple MLP as a default feature extractor. However, you can easily write a custom DNN using [haiku](https://github.com/deepmind/dm-haiku) and pass it to the viDKL initializer
```python3
import haiku as hk

class ConvNet(hk.Module):
    def __init__(self, embedim=2):
        super().__init__()
        self._embedim = embedim   

    def __call__(self, x):
        x = hk.Conv2D(32, 3)(x)
        x = jax.nn.relu(x)
        x = hk.MaxPool(2, 2, 'SAME')(x)
        x = hk.Conv2D(64, 3)(x)
        x = jax.nn.relu(x)
        x = hk.Flatten()(x)
        x = hk.Linear(self._embedim)(x)
        return x

dkl = gpax.viDKL(X.shape[1:], 2, kernel='RBF', nn=ConvNet)  # input data dimensions are (n,h,w,c)
dkl.fit(rng_key, X_train, y_train, num_steps=100, step_size=0.05)
obj = gpax.acquisition.UCB(rng_key_predict, dkl, X_unmeasured, maximize=True)
next_point_idx = obj.argmax()
```
## Installation
If you would like to utilize a GPU acceleration, follow these [instructions](https://github.com/google/jax#installation) to install JAX with a GPU support.

Then, install GPax using pip. We recommend installing the latest stable deployment from PyPI using

```bash
pip install gpax
```

Otherwise, if you are confident in what's on the `main` branch of GPax, you can also install directly from the GitHub repository:

```bash
pip install git+https://github.com/ziatdinovmax/gpax
```

If you are a Windows user, we recommend to use the Windows Subsystem for Linux (WSL2), which comes free on Windows 10 and 11.

## Cite us

If you use GPax in your work, please consider citing our papers:
```
@article{ziatdinov2021physics,
  title={Physics makes the difference: Bayesian optimization and active learning via augmented Gaussian process},
  author={Ziatdinov, Maxim and Ghosh, Ayana and Kalinin, Sergei V},
  journal={arXiv preprint arXiv:2108.10280},
  year={2021}
}

@article{ziatdinov2021hypothesis,
  title={Hypothesis learning in an automated experiment: application to combinatorial materials libraries},
  author={Ziatdinov, Maxim and Liu, Yongtao and Morozovska, Anna N and Eliseev, Eugene A and Zhang, Xiaohang and Takeuchi, Ichiro and Kalinin, Sergei V},
  journal={arXiv preprint arXiv:2112.06649},
  year={2021}
}
```

## Funding acknowledgment
This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences Program.


================================================
FILE: docs/Makefile
================================================
# Minimal makefile for Sphinx documentation
#

# You can set these variables from the command line, and also
# from the environment for the first two.
SPHINXOPTS    ?=
SPHINXBUILD   ?= sphinx-build
SOURCEDIR     = source
BUILDDIR      = build

# Put it first so that "make" without argument is like "make help".
help:
	@$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)

.PHONY: help Makefile

# Catch-all target: route all unknown targets to Sphinx using the new
# "make mode" option.  $(O) is meant as a shortcut for $(SPHINXOPTS).
%: Makefile
	@$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)

================================================
FILE: docs/make.bat
================================================
@ECHO OFF

pushd %~dp0

REM Command file for Sphinx documentation

if "%SPHINXBUILD%" == "" (
	set SPHINXBUILD=sphinx-build
)
set SOURCEDIR=source
set BUILDDIR=build

if "%1" == "" goto help

%SPHINXBUILD% >NUL 2>NUL
if errorlevel 9009 (
	echo.
	echo.The 'sphinx-build' command was not found. Make sure you have Sphinx
	echo.installed, then set the SPHINXBUILD environment variable to point
	echo.to the full path of the 'sphinx-build' executable. Alternatively you
	echo.may add the Sphinx directory to PATH.
	echo.
	echo.If you don't have Sphinx installed, grab it from
	echo.http://sphinx-doc.org/
	exit /b 1
)

%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
goto end

:help
%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%

:end
popd

================================================
FILE: docs/requirements_rtd.txt
================================================
setuptools>=41.0.1
matplotlib>=3.2
sphinx>=3,<7
sphinx_autodoc_typehints>=1.11.0
recommonmark>=0.6.0
sphinx_rtd_theme>=0.5.0
typing-extensions>=4.4.0
jax>=0.4.8
numpyro>=0.11.0
dm-haiku>=0.0.5
dunamai==1.19.2

================================================
FILE: docs/source/LICENSE.rst
================================================
MIT License

Copyright (c) 2024 GPax authors

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

================================================
FILE: docs/source/README.rst
================================================
Installation
============

If you would like to use GPax with a GPU acceleration, follow these `instructions <https://github.com/google/jax#installation>`_ to install JAX with a GPU support.

Then, install GPax using pip as

.. code:: bash

    pip install gpax

for the stable version or

.. code:: bash
    
    pip install git+https://github.com/ziatdinovmax/gpax

to get the most recent updates.

If you are a Windows user, we recommend to use the Windows Subsystem for Linux (WSL2).

================================================
FILE: docs/source/USAGE.rst
================================================
How To Use
==========

Simple GP
---------

1D Example
^^^^^^^^^^

|Open in Colab|

.. |Open in Colab| image:: https://colab.research.google.com/assets/colab-badge.svg
   :target: https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/gpax_simpleGP.ipynb

The code snippet below shows how to use vanilla GP in a fully Bayesian mode. First, we infer GP model parameters from the available training data

.. code:: python

    import gpax
    # Get random number generator keys for training and prediction
    rng_key_train, rng_key_predict = gpax.utils.get_keys()
    # Initialize model
    gp_model = gpax.ExactGP(1, kernel='RBF')
    # Run Hamiltonian Monte Carlo to obtain posterior samples for the GP model parameters
    gp_model.fit(rng_key_train, X, y)  # X and y are numpy arrays with dimensions (n, d) and (n,)

In the fully Bayesian mode, we get a pair of predictive mean and covariance for each Hamiltonian Monte Carlo sample containing the GP parameters (in this case, the RBF kernel hyperparameters and model noise). Hence, a prediction on new inputs with a trained GP model returns the center of the mass of all the predictive means (``y_pred``) and samples from multivariate normal distributions for all the pairs of predictive means and covariances (``y_sampled``).

.. code:: python

    y_pred, y_sampled = gp_model.predict(rng_key_predict, X_test)

.. image:: imgs/GPax_Fig1.jpg
  :alt: GPax_GP1

For 1-dimensional data, we can plot the GP prediction using the standard approach where the uncertainty in predictions - represented by a standard deviation in ``y_sampled`` - is depicted as a shaded area around the mean value.

.. image:: imgs/GPax_Fig2.jpg
  :alt: GPax_GP2

Sparse 2D Image Reconstruction
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

|viGP|

.. |viGP| image:: https://colab.research.google.com/assets/colab-badge.svg
   :target: https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/gpax_viGP.ipynb


One can also use GP for sparse image reconstruction. The fully Bayesian GP is typically too slow for this purpose and it makes sense to use a stochastic variational inference approximation (viGP) instead. Code-wise, the usage of viGP in GPax is almost the same as that of the fully Bayesian GP. One difference is that instead of ``num_samples`` we have ``num_steps``. We can also control the learning rate by specifying a ``step_size``. 

.. code:: python

  # Get training inputs/targets and full image indices from sparse image data
  X_train, y_train, X_full = gpax.utils.preprocess_sparse_image(sparse_img) # sparse_img is a 2D numpy array

  # Initialize and train a variational inference GP model
  gp_model = gpax.viGP(2, kernel='Matern', guide='delta')
  gp_model.fit(rng_key, X_train, y_train, num_steps=250, step_size=0.05)


When we run the ``.predict()`` method, the output is predictive mean and variance computed from a learned single estimate of the GP model parameters:

.. code:: python

  y_pred, y_var = gp_model.predict(rng_key_predict, X_full)

Note that it returns flattened numpy arrays that you will need to reshape back to the original image shape.

.. image:: imgs/viGP.jpg
  :alt: viGP

Finally, for larger images or hyperspecteral data, one can use the `inducing inputs <https://www.jmlr.org/papers/volume6/quinonero-candela05a/quinonero-candela05a.pdf>`_ approximation of viGP, which is also available in GPax.


Structured GP
-------------

|sGP|

.. |sGP| image:: https://colab.research.google.com/assets/colab-badge.svg
   :target: https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/GP_sGP.ipynb

The limitation of the standard GP is that it does not usually allow for the incorporation of prior domain knowledge and can be biased toward a trivial interpolative solution. Recently, we `introduced <https://arxiv.org/abs/2108.10280>`_ a structured Gaussian Process (sGP), where a classical GP is augmented by a structured probabilistic model of the expected system’s behavior. This approach allows us to `balance <https://towardsdatascience.com/unknown-knowns-bayesian-inference-and-structured-gaussian-processes-why-domain-scientists-know-4659b7e924a4>`_ the flexibility of the non-parametric GP approach with a rigid structure of prior (physical) knowledge encoded into the parametric model.
Implementation-wise, we substitute a constant/zero prior mean function in GP with a probabilistic model of the expected system's behavior.

For example, if we have prior knowledge that our objective function has a discontinuous 'phase transition', and a power law-like behavior before and after this transition, we may express it using a simple piecewise function

.. code:: python

    import jax.numpy as jnp

    def piecewise(x: jnp.ndarray, params: Dict[str, float]) -> jnp.ndarray:
        """Power-law behavior before and after the transition"""
        return jnp.piecewise(
            x, [x < params["t"], x >= params["t"]],
            [lambda x: x**params["beta1"], lambda x: x**params["beta2"]])

This function is deterministic. To make it probabilistic, we put priors over its parameters with the help of NumPyro

.. code:: python

    import numpyro
    from numpyro import distributions

    def piecewise_priors():
        # Sample model parameters
        t = numpyro.sample("t", distributions.Uniform(0.5, 2.5))
        beta1 = numpyro.sample("beta1", distributions.Normal(3, 1))
        beta2 = numpyro.sample("beta2", distributions.Normal(3, 1))
        # Return sampled parameters as a dictionary
        return {"t": t, "beta1": beta1, "beta2": beta2}

Finally, we train the sGP model and make predictions on new data in the almost exact same way we did for vanilla GP. The only difference is that we pass our structured probabilistic model as two new arguments (the piecewise function and the corresponding priors over its parameters) when initializing GP.

.. code:: python

    # Get random number generator keys
    rng_key_train, rng_key_predict = gpax.utils.get_keys()
    # Initialize structured GP model
    sgp_model = gpax.ExactGP(1, kernel='Matern', mean_fn=piecewise, mean_fn_prior=piecewise_priors)
    # Run MCMC to obtain posterior samples
    sgp_model.fit(rng_key_train, X, y)
    # Get GP prediction on new/test data
    y_pred, y_sampled = sgp_model.predict(rng_key_predict, X_test)

.. image:: imgs/GP_vs_sGP2.jpg
  :alt: GPax_sGP

Structured GP is usually better at extrapolation and provides more reasonable uncertainty estimates. The probabilistic model in structured GP reflects our prior knowledge about the system, but it does not have to be precise, that is, the model can have a different functional form, as long as it captures general or partial trends in the data. 

Active learning & Bayesian optimization
---------------------------------------

|BO|

.. |BO| image:: https://colab.research.google.com/assets/colab-badge.svg
   :target: https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/gpax_GPBO.ipynb


Both GP and sGP can be used for active learning to reconstruct the entire data distribution from sparse observations or to localize regions of the parameter space where a particular physical behavior is maximized or minimized with as few measurements as possible.

.. code:: python

  # Train a GP model (it can be sGP or vanilla GP)
  gp_model.fit(rng_key, X_measured, y_measured)  # A

  # Compute the upper confidence bound (UCB) acquisition function to derive the next measurement point
  acq = gpax.acquisition.UCB(rng_key_predict, gp_model, X_unmeasured, beta=4, maximize=False, noiseless=True)  # B
  next_point_idx = acq.argmax()  # C
  next_point = X_unmeasured[next_point_idx]  # D

  # Perform measurement in next_point, update measured & unmeasured data arrays, and re-run steps A-D.

In the figure below we illustrate the connection between the (s)GP posterior predictive distribution and the acquisition function used to derive the next measurement points. Here, the posterior mean values indicate that the minimum of a "black box" function describing a behavior of interest is around $x=0.7$. At the same time, there is a large dispersion in the samples from the posterior predictive distribution between $x=-0.5$ and $x=0.5$, resulting in high uncertainty in that region. The acquisition function is computed as a function of both predictive mean and uncertainty and its maximum corresponds to the next measurement point in the active learning and Bayesian optimization. Here, after taking into account the uncertainty in the prediction, the UCB acquisition function suggests exploring a point at x≈0 where potentially a true minimum is located.

.. image:: imgs/GP_BO2.png
  :alt: GPax_BO


Theory-informed data reconstruction and Bayesian optimization
-------------------------------------------------------------

|MTGP|

.. |MTGP| image:: https://colab.research.google.com/assets/colab-badge.svg
   :target: https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/GPax_MultiTaskGP_BO.ipynb

Sometimes when theoretical simulations are available before the experiment, they can be used to guide the measurements or simply reconstruct sparse data via a multi-task/fidelity Gaussian process. This can be an alternative to a structured Gaussian process in situations where a mean function is too costly to compute at each step or it is expressed through some complex program that is not fully differentiable. The overall scheme is the same, but now our GP model is a MultitaskGP:

.. code:: python

  key1, key2 = gpax.utils.get_keys(1)

  gp_model = gpax.MultiTaskGP(
      input_dim=1, data_kernel='Matern',  # standard GP parameters
      shared_input_space=False,  # different tasks/fidelities have different numbers of observations
      num_latents=2, rank=2,  # parameters of multi-task GP
  )

  model.fit(key1, X, y, num_warmup=500, num_samples=500)

Note that X has (N, D+1) dimensions where the last column contains task/fidelity indices for each observation. We can then use the trained model to reconstruct data from partial (expensive) observations:

.. code:: python

  # Create a set of inputs for the task/fidelity 2
  X_unmeasured2 = np.column_stack((X_full_range, np.ones_like(X_full_range)))

  # Make a prediction with the trained model
  y_mean2, y_sampled2 = model.predict(key2, X_unmeasured2, noiseless=True)

.. image:: imgs/GP_vs_MTGP.jpg
  :alt: GP_vs_MTGP

Hypothesis learning
-------------------

|hypoAL|

.. |hypoAL| image:: https://colab.research.google.com/assets/colab-badge.svg
   :target: https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/gpax_hypo.ipynb

The structured GP can be also used for hypothesis learning in automated experiments. The `hypothesis learning <https://arxiv.org/abs/2112.06649>`_ is based on the idea that in active learning, the correct model of the system’s behavior leads to a faster decrease in the overall Bayesian uncertainty about the system under study. In the hypothesis learning setup, probabilistic models of the possible system’s behaviors (hypotheses) are wrapped into structured GPs, and a basic reinforcement learning policy is used to select a correct model from several competing hypotheses. A full example is available `here <https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/hypoAL.ipynb>`_.

.. image:: imgs/HypoAL.gif
  :alt: GPax_HypoAL

Deep Kernel Learning
--------------------

|DKL|

.. |DKL| image:: https://colab.research.google.com/assets/colab-badge.svg
   :target: https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/gpax_viDKL_plasmons.ipynb

`Deep Kernel Learning <https://arxiv.org/abs/1511.02222>`_ can be understood as a hybrid of deep neural network (DNN) and GP. The DNN serves as a feature extractor that allows reducing the complex high-dimensional features to low-dimensional descriptors on which a standard GP kernel operates. The parameters of DNN and of GP kernel are inferred jointly in an end-to-end fashion. Practically, the DKL training inputs are usually patches from an (easy-to-acquire) structural image, and training targets represent a physical property of interest derived from the (hard-to-acquire) spectra measured in those patches. The DKL output on the new inputs (image patches for which there are no measured spectra) is the expected property value and associated uncertainty, which can be used to derive the next measurement point in the automated experiment.

.. code:: python
  
  import gpax

  # Get random number generator keys for training and prediction
  rng_key, rng_key_predict = gpax.utils.get_keys()

  # Obtain/update DKL posterior; input data dimensions are (n, h*w*c)
  dkl = gpax.viDKL(input_dim=X.shape[-1], z_dim=2, kernel='RBF')  # A
  dkl.fit(rng_key, X_train, y_train, num_steps=100, step_size=0.05)  # B

  # Compute UCB acquisition function
  obj = gpax.acquisition.UCB(rng_key_predict, dkl, X_unmeasured, maximize=True)  # C
  # Select next point to measure (assuming grid data)
  next_point_idx = obj.argmax()  # D

  # Perform measurement in next_point_idx, update measured & unmeasured data arrays, and re-run steps A-D.

Below we show a result of a simple DKL-based search for regions of the nano-plasmonic array that host a specific plasmon mode

.. image:: imgs/DKL_STEM.png
  :alt: GPax_DKL

Note that in viDKL, we use a simple MLP as a default feature extractor. However, you can easily write a custom DNN using `haiku <https://github.com/deepmind/dm-haiku>`_ and pass it to the viDKL initializer

.. code:: python

  import haiku as hk

  class ConvNet(hk.Module):
      def __init__(self, embedim=2):
          super().__init__()
          self._embedim = embedim   

      def __call__(self, x):
          x = hk.Conv2D(32, 3)(x)
          x = jax.nn.relu(x)
          x = hk.MaxPool(2, 2, 'SAME')(x)
          x = hk.Conv2D(64, 3)(x)
          x = jax.nn.relu(x)
          x = hk.Flatten()(x)
          x = hk.Linear(self._embedim)(x)
          return x

  dkl = gpax.viDKL(X.shape[1:], 2, kernel='RBF', nn=ConvNet)  # input data dimensions are (n,h,w,c)
  dkl.fit(rng_key, X_train, y_train, num_steps=100, step_size=0.05)
  obj = gpax.acquisition.UCB(rng_key_predict, dkl, X_unmeasured, maximize=True)
  next_point_idx = obj.argmax()


================================================
FILE: docs/source/acquisition.rst
================================================
Acquisition functions
=====================

.. autofunction:: gpax.acquisition.UCB

.. autofunction:: gpax.acquisition.EI

.. autofunction:: gpax.acquisition.POI
  
.. autofunction:: gpax.acquisition.UE

.. autofunction:: gpax.acquisition.Thompson

.. autofunction:: gpax.acquisition.KG
  
.. autofunction:: gpax.acquisition.qUCB

.. autofunction:: gpax.acquisition.qEI

.. autofunction:: gpax.acquisition.qPOI

.. autofunction:: gpax.acquisition.qKG

.. autofunction:: gpax.acquisition.optimize_acq

================================================
FILE: docs/source/conf.py
================================================
# Configuration file for the Sphinx documentation builder.
#
# This file only contains a selection of the most common options. For a full
# list see the documentation:
# https://www.sphinx-doc.org/en/master/usage/configuration.html

# -- Path setup --------------------------------------------------------------

# If extensions (or modules to document with autodoc) are in another directory,
# add these directories to sys.path here. If the directory is relative to the
# documentation root, use os.path.abspath to make it absolute, like shown here.
#
import os
import sys
sys.path.insert(0, os.path.abspath('../../'))
from gpax._version import __version__

#autodoc_mock_imports = ['jax', 'jax.numpy', 'jax.random', 'numpyro', 'jaxlib',
#                        'numpyro.distributions', 'numpyro.infer', 'haiku', 'numpy']

# -- Project information -----------------------------------------------------

project = 'GPax'
copyright = '2024, GPax authors'
author = 'GPax authors'

# The full version, including alpha/beta/rc tags
release = __version__

# -- General configuration ---------------------------------------------------

# Add any Sphinx extension module names here, as strings. They can be
# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
# ones.
extensions = [
    'sphinx.ext.autodoc',
    'sphinx.ext.doctest',
    'sphinx.ext.coverage',
    'sphinx.ext.githubpages',
    'sphinx.ext.napoleon',
    'sphinx_autodoc_typehints',
    'recommonmark',
    'sphinx.ext.viewcode',
    'sphinx.ext.mathjax'
]

napoleon_use_ivar = True

# Add any paths that contain templates here, relative to this directory.
templates_path = ['_templates']

# The suffix(es) of source filenames.
# You can specify multiple suffix as a list of string:
#
# source_suffix = ['.rst', '.md']
source_suffix = '.rst'

# The master toctree document.
master_doc = 'index'

# The language for content autogenerated by Sphinx. Refer to documentation
# for a list of supported languages.
#
# This is also used if you do content translation via gettext catalogs.
# Usually you set "language" from the command line for these cases.
language = None

# List of patterns, relative to source directory, that match files and
# directories to ignore when looking for source files.
# This pattern also affects html_static_path and html_extra_path .
exclude_patterns = ['_build', 'Thumbs.db', '.DS_Store']

# The name of the Pygments (syntax highlighting) style to use.
pygments_style = 'sphinx'

autodoc_default_options = {
    'exclude-members': 'forward'
}
# -- Options for HTML output -------------------------------------------------

# The theme to use for HTML and HTML Help pages.  See the documentation for
# a list of builtin themes.
#
# html_theme = 'alabaster'
html_theme = 'sphinx_rtd_theme'


# Theme options are theme-specific and customize the look and feel of a theme
# further.  For a list of options available for each theme, see the
# documentation.
#
# html_theme_options = {}

# Add any paths that contain custom static files (such as style sheets) here,
# relative to this directory. They are copied after the builtin static files,
# so a file named "default.css" will overwrite the builtin "default.css".
html_static_path = ['_static']

# Custom sidebar templates, must be a dictionary that maps document names
# to template names.
#
# The default sidebars (for documents that don't match any pattern) are
# defined by theme itself.  Builtin themes are using these templates by
# default: ``['localtoc.html', 'relations.html', 'sourcelink.html',
# 'searchbox.html']``.
#
# html_sidebars = {}


# -- Options for HTMLHelp output ---------------------------------------------

# Output file base name for HTML help builder.
htmlhelp_basename = 'indexedconvdoc'


# -- Options for LaTeX output ------------------------------------------------

latex_elements = {
    # The paper size ('letterpaper' or 'a4paper').
    #
    # 'papersize': 'letterpaper',

    # The font size ('10pt', '11pt' or '12pt').
    #
    # 'pointsize': '10pt',

    # Additional stuff for the LaTeX preamble.
    #
    # 'preamble': '',

    # Latex figure (float) alignment
    #
    # 'figure_align': 'htbp',
}

# Grouping the document tree into LaTeX files. List of tuples
# (source start file, target name, title,
#  author, documentclass [howto, manual, or own class]).
latex_documents = [
    (master_doc, 'indexedconv.tex', 'indexedconv Documentation',
     'Mikael Jacquemont, Thomas Vuillaume, Luca Antiga', 'manual'),
]


# -- Options for manual page output ------------------------------------------

# One entry per manual page. List of tuples
# (source start file, name, description, authors, manual section).
man_pages = [
    (master_doc, 'indexedconv', 'indexedconv Documentation',
     [author], 1)
]


# -- Options for Texinfo output ----------------------------------------------

# Grouping the document tree into Texinfo files. List of tuples
# (source start file, target name, title, author,
#  dir menu entry, description, category)
texinfo_documents = [
    (master_doc, 'indexedconv', 'indexedconv Documentation',
     author, 'indexedconv', 'One line description of project.',
     'Miscellaneous'),
]


# -- Extension configuration -------------------------------------------------

================================================
FILE: docs/source/examples.rst
================================================
Colab notebooks
===============

The easiest way to start using GPax is via Google Colab, which is a free research tool from Google for machine learning education and research built on top of Jupyter Notebook. The following notebooks can be executed in Google Colab by simply clicking on the "Open in Colab" icon:

*   | Gaussian process in the fully Bayesian mode |simpleGP|

*   | Structured Gaussian processes |sGP|

*   | Bayesian optimization |GPBO|

*   | Theory-informed Gaussian process & Bayesian optimization |MTGPBO|

*   | Hypothesis learning |hypoAL|

*   | Deep Kernel Learning |DKL|

*   | Heteroskedastic Gaussian processes |VarNoiseGP|

.. |simpleGP| image:: https://colab.research.google.com/assets/colab-badge.svg
   :target: https://colab.research.google.com/github/ziatdinovmax/gpax/blob/master/examples/simpleGP.ipynb

.. |sGP| image:: https://colab.research.google.com/assets/colab-badge.svg
   :target: https://colab.research.google.com/github/ziatdinovmax/gpax/blob/master/examples/GP_sGP.ipynb

.. |GPBO| image:: https://colab.research.google.com/assets/colab-badge.svg
   :target: https://colab.research.google.com/github/ziatdinovmax/gpax/blob/master/examples/gpax_GPBO.ipynb

.. |MTGPBO| image:: https://colab.research.google.com/assets/colab-badge.svg
   :target: https://colab.research.google.com/github/ziatdinovmax/gpax/blob/master/examples/GPax_MultiTaskGP_BO.ipynb

.. |hypoAL| image:: https://colab.research.google.com/assets/colab-badge.svg
   :target: https://colab.research.google.com/github/ziatdinovmax/gpax/blob/master/examples/hypoAL.ipynb
   
.. |DKL| image:: https://colab.research.google.com/assets/colab-badge.svg
   :target: https://colab.research.google.com/github/ziatdinovmax/gpax/blob/master/examples/gpax_viDKL_plasmons.ipynb

.. |VarNoiseGP| image:: https://colab.research.google.com/assets/colab-badge.svg
   :target: https://colab.research.google.com/github/ziatdinovmax/gpax/blob/master/examples/heteroskedasticGP.ipynb


================================================
FILE: docs/source/hypo.rst
================================================
Hypothesis learning
===================

.. autofunction:: gpax.hypo.step

.. autofunction:: gpax.hypo.sample_next

.. autofunction:: gpax.hypo.softmax

.. autofunction:: gpax.hypo.eps_greedy

.. autofunction:: gpax.hypo.update_record

================================================
FILE: docs/source/index.rst
================================================
GPax: Gaussian Processes for Experimental Sciences
==================================================

GPax is a small Python package for physics-based Gaussian processes (GPs) built on top of NumPyro and JAX. Its purpose is to take advantage of prior physical knowledge and different data modalities when using GPs for data reconstruction and active learning. It is a work in progress, and more models will be added in the near future.

.. image:: imgs/GPax_v2.jpg
  :alt: GPax

.. toctree::
   :maxdepth: 3
   :caption: Notes

   README.rst
   LICENSE.rst
   USAGE.rst

.. toctree::
   :glob:
   :caption: Package Content

   models
   acquisition
   kernels
   priors
   hypo
   utils

.. toctree::
   :maxdepth: 3
   :caption: Examples

   examples 


================================================
FILE: docs/source/kernels.rst
================================================
Kernels
=======

.. autofunction:: gpax.kernels.RBFKernel

.. autofunction:: gpax.kernels.MaternKernel

.. autofunction:: gpax.kernels.PeriodicKernel

.. autofunction:: gpax.kernels.NNGPKernel

.. autofunction:: gpax.kernels.MultitaskKernel

.. autofunction:: gpax.kernels.MultivariateKernel

.. autofunction:: gpax.kernels.LCMKernel

================================================
FILE: docs/source/models.rst
================================================
GPax models
===========

Gaussian Processes - Fully Bayesian Implementation
--------------------------------------------------
.. autoclass:: gpax.models.gp.ExactGP
    :members:
    :inherited-members:
    :undoc-members:
    :member-order: bysource
    :show-inheritance:

.. autoclass:: gpax.models.uigp.UIGP
    :members:
    :inherited-members:
    :undoc-members:
    :member-order: bysource
    :show-inheritance:

.. autoclass:: gpax.models.hskgp.VarNoiseGP
    :members:
    :inherited-members:
    :undoc-members:
    :member-order: bysource
    :show-inheritance:

.. autoclass:: gpax.models.mngp.MeasuredNoiseGP
    :members:
    :inherited-members:
    :undoc-members:
    :member-order: bysource
    :show-inheritance:

.. autoclass:: gpax.models.vgp.vExactGP
    :members:
    :inherited-members:
    :undoc-members:
    :member-order: bysource
    :show-inheritance:

Gaussian Processes - Approximate Bayesian
------------------------------------------
.. autoclass:: gpax.models.vigp.viGP
    :members:
    :inherited-members:
    :undoc-members:
    :member-order: bysource
    :show-inheritance:

.. autoclass:: gpax.models.sparse_gp.viSparseGP
    :members:
    :inherited-members:
    :undoc-members:
    :member-order: bysource
    :show-inheritance:

Deep Kernel Learning - Fully Bayesian Implementation
----------------------------------------------------
.. autoclass:: gpax.models.dkl.DKL
    :members:
    :inherited-members:
    :undoc-members:
    :member-order: bysource
    :show-inheritance:

Deep Kernel Learning - Approximate Bayesian
-------------------------------------------
.. autoclass:: gpax.models.vidkl.viDKL
    :members:
    :inherited-members:
    :undoc-members:
    :member-order: bysource
    :show-inheritance:

Infinite-width Bayesian Neural Networks
----------------------------------------
.. autoclass:: gpax.models.ibnn.iBNN
    :members:
    :inherited-members:
    :undoc-members:
    :member-order: bysource
    :show-inheritance:

Multi-Task Learning
--------------------
.. autoclass:: gpax.models.mtgp.MultiTaskGP
    :members:
    :inherited-members:
    :undoc-members:
    :member-order: bysource
    :show-inheritance:

.. autoclass:: gpax.models.vi_mtdkl.viMTDKL
    :members:
    :inherited-members:
    :undoc-members:
    :member-order: bysource
    :show-inheritance:

Structured Probabilistic Models
-------------------------------
.. autoclass:: gpax.models.spm.sPM
    :members:
    :inherited-members:
    :undoc-members:
    :member-order: bysource
    :show-inheritance:



================================================
FILE: docs/source/priors.rst
================================================
Priors
======

.. autofunction:: gpax.priors.normal_dist

.. autofunction:: gpax.priors.lognormal_dist

.. autofunction:: gpax.priors.halfnormal_dist

.. autofunction:: gpax.priors.gamma_dist

.. autofunction:: gpax.priors.uniform_dist

.. autofunction:: gpax.priors.auto_normal_priors

.. autofunction:: gpax.priors.auto_lognormal_priors

.. autofunction:: gpax.priors.auto_normal_kernel_priors

.. autofunction:: gpax.priors.auto_lognormal_kernel_priors





================================================
FILE: docs/source/utils.rst
================================================
Utilities
=========

Automatic function setters
--------------------------

.. autofunction:: gpax.utils.set_fn

.. autofunction:: gpax.utils.set_kernel_fn


Other utilities
---------------

.. autofunction:: gpax.utils.dviz

.. autofunction:: gpax.utils.get_keys

.. autofunction:: gpax.utils.enable_x64

================================================
FILE: examples/GP_sGP.ipynb
================================================
{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/GP_sGP.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "136rQl-Z67Xf"
      },
      "outputs": [],
      "source": [
        "# For github continuous integration\n",
        "import os\n",
        "if os.environ.get(\"CI_SMOKE\"):\n",
        "    NUM_WARMUP = 10\n",
        "    NUM_SAMPLES = 10\n",
        "else:\n",
        "    NUM_WARMUP = 2000\n",
        "    NUM_SAMPLES = 2000"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NtiDY7RcohrR"
      },
      "source": [
        "# Structured Gaussian Process\n",
        "\n",
        "This notebook compares vanilla and structured Gaussian processes for reconstructing and active learning of function characterized by a discontinuous behavior at some \"transition\" point.\n",
        "\n",
        "*Prepared by Maxim Ziatdinov (2022). Last updated in October 2023.*"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vUoeZ9Tin74Q"
      },
      "source": [
        "In the previous [example](https://colab.research.google.com/github/ziatdinovmax/gpax/blob/main/examples/simpleGP.ipynb), we have introduced Gaussian process (GP) operating in a fully Bayesian mode for reconstucting, with quantified uncertainty, an unknown function from sparse measurements. The limitation of the standard GP is that it does not usually allow for the incorporation of prior domain knowledge and can be biased toward a trivial interpolative solution. Recently, we introduced a structured Gaussian Process (sGP), where a classical GP is augmented by a structured probabilistic model of the expected system’s behavior. This approach allows us to balance the flexibility of the non-parametric GP approach with a rigid structure of prior (physical) knowledge encoded into the parametric model. Implementation-wise, this is achieved by substituting a zero prior mean function in GP with a probabilistic model of the expected system's behavior."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HdtH0tCPQ2de"
      },
      "source": [
        "## Install & Import"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "86iUwKxLO7qE"
      },
      "source": [
        "Install the latest GPax package from PyPI (this is best practice, as it installs the latest, deployed and tested version)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VQ1rLUzqha2i"
      },
      "outputs": [],
      "source": [
        "!pip install -q gpax"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vygoK7MTjJWB"
      },
      "source": [
        "Import needed packages:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XCoyWlKt67Xk"
      },
      "outputs": [],
      "source": [
        "try:\n",
        "    # For use on Google Colab\n",
        "    import gpax\n",
        "\n",
        "except ImportError:\n",
        "    # For use locally (where you're using the local version of gpax)\n",
        "    print(\"Assuming notebook is being run locally, attempting to import local gpax module\")\n",
        "    import sys\n",
        "    sys.path.append(\"..\")\n",
        "    import gpax"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KtGDc11Ehh7r"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "gpax.utils.enable_x64()  # enable double precision"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G6cPAvHh67Xk"
      },
      "source": [
        "Enable some pretty plotting."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "V5isV5Ho67Xl"
      },
      "outputs": [],
      "source": [
        "import matplotlib as mpl"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gUyKDZjM67Xl"
      },
      "outputs": [],
      "source": [
        "mpl.rcParams['mathtext.fontset'] = 'stix'\n",
        "mpl.rcParams['font.family'] = 'STIXGeneral'\n",
        "mpl.rcParams['text.usetex'] = False\n",
        "plt.rc('xtick', labelsize=12)\n",
        "plt.rc('ytick', labelsize=12)\n",
        "plt.rc('axes', labelsize=12)\n",
        "mpl.rcParams['figure.dpi'] = 200"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZSaWCRHJPukv"
      },
      "source": [
        "## Standard and structured GP"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D6vVHZKpxse_"
      },
      "source": [
        "We consider noisy observations of a discontinuous function..."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LAvbGDom67Xl"
      },
      "outputs": [],
      "source": [
        "def piecewise1(x: np.ndarray, params) -> np.ndarray:\n",
        "    return np.piecewise(\n",
        "        x,\n",
        "        [x < params[\"t\"], x >= params[\"t\"]],\n",
        "        [lambda x: x**params[\"beta1\"], lambda x: x**params[\"beta2\"]])\n",
        "\n",
        "\n",
        "NUM_INIT_POINTS = 15 # number of observation points\n",
        "NOISE_LEVEL = 0.1\n",
        "PARAMS = {\"t\": 1.7, \"beta1\": 4.5, \"beta2\": 2.5}\n",
        "\n",
        "np.random.seed(1)\n",
        "X = np.random.uniform(0, 3, NUM_INIT_POINTS)\n",
        "y = piecewise1(X, PARAMS) + np.random.normal(0., NOISE_LEVEL, NUM_INIT_POINTS)\n",
        "\n",
        "X_test = np.linspace(0, 3, 200)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 454
        },
        "id": "LF2l_UcBtaDT",
        "outputId": "bd7d82d4-4d2a-482a-97c4-5d289dfe352e"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x400 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ],
      "source": [
        "_, ax = plt.subplots(1, 1, figsize=(6, 2))\n",
        "ax.scatter(X, y, alpha=0.5, c='k', marker='x', label=\"Noisy observations\")\n",
        "ax.legend()\n",
        "ax.set_xlabel(\"$x$\")\n",
        "ax.set_ylabel(\"$y$\")\n",
        "ax.set_xlim(0, 3)\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rPfkj1cRQLop"
      },
      "source": [
        "... and try to reconstruct this underlying function with a standard GP"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cOtfzDCo0MMI",
        "outputId": "82dda990-6cd0-407d-d6fb-18abdadbb212"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "sample: 100%|██████████| 4000/4000 [00:13<00:00, 299.14it/s, 7 steps of size 6.22e-01. acc. prob=0.90]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "                 mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
            "k_length[0]      0.61      0.17      0.58      0.40      0.80    549.76      1.00\n",
            "    k_scale     19.08      9.91     16.54      7.12     31.91    915.50      1.00\n",
            "      noise      0.28      0.39      0.17      0.01      0.58    555.31      1.00\n",
            "\n"
          ]
        }
      ],
      "source": [
        "# Get random number generator keys (see JAX documentation for why it is neccessary)\n",
        "rng_key, rng_key_predict = gpax.utils.get_keys()\n",
        "\n",
        "# Initialize model\n",
        "gp_model = gpax.ExactGP(1, kernel='Matern')\n",
        "\n",
        "# Run HMC to obtain posterior samples\n",
        "gp_model.fit(rng_key, X, y, num_chains=1)\n",
        "\n",
        "# Get GP prediction\n",
        "posterior_mean, f_samples = gp_model.predict(rng_key_predict, X_test, n=200)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hzSJnqOH67Xm"
      },
      "source": [
        "Plot the results"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lnxdYcLL67Xm",
        "outputId": "584a3a74-32e5-4f13-d3e5-0d2bcdf9cfe7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 454
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x400 with 1 Axes>"
            ],
            "image/png": 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