<div style="text-align:center">
<img width="500" height="200" src="https://github.com/GPflow/GPflow/blob/develop/doc/sphinx/_static/gpflow_logo.svg">
</div>
[](https://circleci.com/gh/GPflow/GPflow/tree/develop)
[](http://codecov.io/github/GPflow/GPflow?branch=master)
[](https://join.slack.com/t/gpflow/shared_invite/enQtOTE5MDA0Nzg5NjA2LTYwZWI3MzhjYjNlZWI1MWExYzZjMGNhOWIwZWMzMGY0YjVkYzAyYjQ4NjgzNDUyZTgyNzcwYjAyY2QzMWRmYjE)
[Website](https://gpflow.org) |
[Documentation (release)](https://gpflow.github.io/GPflow/) |
[Documentation (develop)](https://gpflow.github.io/GPflow/develop) |
[Glossary](GLOSSARY.md)
#### Table of Contents
<!-- created with help from https://github.com/ekalinin/github-markdown-toc and further manual adjustments -->
* [What does GPflow do?](#what-does-gpflow-do)
* [Installation](#installation)
* [Getting Started with GPflow 2.0](#getting-started-with-gpflow-20)
* [The GPflow Community](#the-gpflow-community)
* [Getting help](#getting-help)
* [Slack workspace](#slack-workspace)
* [Contributing](#contributing)
* [Projects using GPflow](#projects-using-gpflow)
* [Version Compatibility](#version-compatibility)
* [TensorFlow 1.x and GPflow 1.x](#tensorflow-1x-and-gpflow-1x)
* [Citing GPflow](#citing-gpflow)
## What does GPflow do?
GPflow is a package for building Gaussian process models in Python.
It implements modern Gaussian process inference for composable kernels and likelihoods.
GPflow builds on [TensorFlow 2.4+](http://www.tensorflow.org) and [TensorFlow Probability](https://www.tensorflow.org/probability/) for running computations, which allows fast execution on GPUs.
The [online documentation (latest release)](https://gpflow.github.io/GPflow/)/[(develop)](https://gpflow.github.io/GPflow/develop) contains more details.
### Maintainers
It was originally created by [James Hensman](http://jameshensman.github.io/) and [Alexander G. de G. Matthews](https://github.com/alexggmatthews).
It is now actively maintained by (in alphabetical order)
[Artem Artemev](http://github.com/awav/),
[Mark van der Wilk](https://markvdw.github.io/),
[ST John](https://github.com/st--),
and [Vincent Dutordoir](https://vdutor.github.io/).
GPflow would not be the same without the community. **We are grateful to [all contributors](CONTRIBUTORS.md) who have helped shape GPflow.**
*GPflow is an open source project. If you have relevant skills and are interested in contributing then please do contact us (see ["The GPflow community" section](#the-gpflow-community) below).*
## Installation
### Requirements
GPflow depends on both TensorFlow (TF, version ≥ 2.4) and TensorFlow Probability (TFP, version ≥ 0.12). We support Python ≥ 3.7.
**NOTE:** TensorFlow Probability releases are tightly coupled to TensorFlow, e.g. TFP 0.14 requires TF>=2.6, TFP 0.13 requires TF>=2.5, and TFP 0.12 requires TF>=2.4. Unfortunately, this is _not_ specified in TFP's dependencies. So if you already have an (older) version of TensorFlow installed, GPflow will pull in the latest TFP, which will be incompatible. If you get errors such as `ImportError: This version of TensorFlow Probability requires TensorFlow version >= 2.4`, you have to either upgrade TensorFlow (`pip install -U tensorflow`) or manually install an older version of the `tensorflow_probability` package.
### Latest (stable) release from PyPI
```bash
pip install gpflow
```
### Latest (bleeding-edge) source from GitHub
*Be aware that the `develop` branch may change regularly, and new commits may break your code.*
In a check-out of the `develop` branch of the [GPflow GitHub repository](https://github.com/GPflow/GPflow), run
```bash
pip install -e .
```
Alternatively, you can install the latest GitHub `develop` version using `pip`:
```bash
pip install git+https://github.com/GPflow/GPflow.git@develop#egg=gpflow
```
This will automatically install all required dependencies.
## Getting Started with GPflow 2.0
There is an ["Intro to GPflow 2.0"](https://gpflow.github.io/GPflow/develop/notebooks/intro_to_gpflow2.html) Jupyter notebook; check it out for details.
To convert your code from GPflow 1 check the [GPflow 2 upgrade guide](https://gpflow.github.io/GPflow/develop/notebooks/gpflow2_upgrade_guide.html).
## The GPflow Community
### Getting help
**Bugs, feature requests, pain points, annoying design quirks, etc:**
Please use [GitHub issues](https://github.com/GPflow/GPflow/issues/) to flag up bugs/issues/pain points, suggest new features, and discuss anything else related to the use of GPflow that in some sense involves changing the GPflow code itself.
You can make use of the [labels](https://github.com/GPflow/GPflow/labels) such as [`bug`](https://github.com/GPflow/GPflow/labels/bug), [`discussion`](https://github.com/GPflow/GPflow/labels/discussion), [`feature`](https://github.com/GPflow/GPflow/labels/feature), [`feedback`](https://github.com/GPflow/GPflow/labels/feedback), etc.
We positively welcome comments or concerns about usability, and suggestions for changes at any level of design.
We aim to respond to issues promptly, but if you believe we may have forgotten about an issue, please feel free to add another comment to remind us.
**"How-to-use" questions:**
Please use [Stack Overflow (gpflow tag)](https://stackoverflow.com/tags/gpflow) to ask questions that relate to "how to use GPflow", i.e. questions of understanding rather than issues that require changing GPflow code. (If you are unsure where to ask, you are always welcome to open a GitHub issue; we may then ask you to move your question to Stack Overflow.)
### Slack workspace
We have a public [GPflow slack workspace](https://gpflow.slack.com/). Please use this [invite link](https://join.slack.com/t/gpflow/shared_invite/enQtOTE5MDA0Nzg5NjA2LTYwZWI3MzhjYjNlZWI1MWExYzZjMGNhOWIwZWMzMGY0YjVkYzAyYjQ4NjgzNDUyZTgyNzcwYjAyY2QzMWRmYjE) if you'd like to join, whether to ask short informal questions or to be involved in the discussion and future development of GPflow.
### Contributing
All constructive input is gratefully received. For more information, see the [notes for contributors](CONTRIBUTING.md).
### Projects using GPflow
Projects building on GPflow and demonstrating its usage are listed below. The following projects are based on the current GPflow 2.x release:
| Project | Description |
| --- | --- |
| [Trieste](https://github.com/secondmind-labs/trieste) | Bayesian optimization with TensorFlow, with out-of-the-box support for GPflow (2.x) models. |
| [VFF](https://github.com/st--/VFF) | Variational Fourier Features for Gaussian Processes (GPflow 2.x version) |
| [BranchedGP](https://github.com/ManchesterBioinference/BranchedGP) | Gaussian processes with branching kernels.|
| [VBPP](https://github.com/st--/vbpp) | Implementation of "Variational Bayes for Point Processes".|
| [Gaussian Process Regression on Molecules](https://medium.com/@ryangriff123/gaussian-process-regression-on-molecules-in-gpflow-ee6fedab2130) | GPs to predict molecular properties by creating a custom-defined Tanimoto kernel to operate on Morgan fingerprints |
If you would like your project listed here, let us know - or simply [open a pull request](https://github.com/GPflow/GPflow/compare) that adds your project to the table above!
*The following projects build on older versions of GPflow (pre-2020); we encourage their authors to upgrade to GPflow 2.*
| Project | Description |
| --- | --- |
| [GPflowOpt](https://github.com/GPflow/GPflowOpt) | Bayesian Optimization using GPflow (stable release requires GPflow 0.5). |
| [Doubly-Stochastic-DGP](https://github.com/ICL-SML/Doubly-Stochastic-DGP)| Deep Gaussian Processes with Doubly Stochastic Variational Inference.|
| [widedeepnetworks](https://github.com/widedeepnetworks/widedeepnetworks) | Measuring the relationship between random wide deep neural networks and GPs.|
| [orth_decoupled_var_gps](https://github.com/hughsalimbeni/orth_decoupled_var_gps) | Variationally sparse GPs with orthogonally decoupled bases|
| [kernel_learning](https://github.com/frgsimpson/kernel_learning) | Implementation of "Differentiable Compositional Kernel Learning for Gaussian Processes".|
| [DGPs_with_IWVI](https://github.com/hughsalimbeni/DGPs_with_IWVI) | Deep Gaussian Processes with Importance-Weighted Variational Inference|
| [kerndisc](https://github.com/BracketJohn/kernDisc) | Library for automated kernel structure discovery in univariate data|
| [Signature covariances](https://github.com/tgcsaba/GPSig) | kernels for (time)series as *inputs* |
| [Structured-DGP](https://github.com/boschresearch/Structured_DGP) | Adding more structure to the variational posterior of the Doubly Stochastic Deep Gaussian Process |
## Version Compatibility
GPflow heavily depends on TensorFlow and as far as TensorFlow supports forward compatibility, GPflow should as well. The version of GPflow can give you a hint about backward compatibility. If the major version has changed then you need to check the release notes to find out how the API has been changed.
Unfortunately, there is no such thing as backward compatibility for GPflow _models_, which means that a model implementation can change without changing interfaces. In other words, the TensorFlow graph can be different for the same models from different versions of GPflow.
### TensorFlow 1.x and GPflow 1.x
We have stopped development and support for GPflow based on TensorFlow 1.
The latest release supporting TensorFlow 1 is [v1.5.1](https://github.com/GPflow/GPflow/releases/tag/v1.5.1).
[Documentation](https://gpflow.readthedocs.io/en/v1.5.1-docs/) and
[tutorials](https://nbviewer.jupyter.org/github/GPflow/GPflow/blob/v1.5.1/doc/sphinx/notebooks/intro.ipynb)
will remain available.
## Citing GPflow
To cite GPflow, please reference the [JMLR paper](http://www.jmlr.org/papers/volume18/16-537/16-537.pdf). Sample Bibtex is given below:
```
@ARTICLE{GPflow2017,
author = {Matthews, Alexander G. de G. and {van der Wilk}, Mark and Nickson, Tom and
Fujii, Keisuke. and {Boukouvalas}, Alexis and {Le{\'o}n-Villagr{\'a}}, Pablo and
Ghahramani, Zoubin and Hensman, James},
title = "{{GP}flow: A {G}aussian process library using {T}ensor{F}low}",
journal = {Journal of Machine Learning Research},
year = {2017},
month = {apr},
volume = {18},
number = {40},
pages = {1-6},
url = {http://jmlr.org/papers/v18/16-537.html}
}
```
Since the publication of the GPflow paper, the software has been significantly extended
with the framework for interdomain approximations and multioutput priors. We review the
framework and describe the design in an [arXiv paper](https://arxiv.org/abs/2003.01115),
which can be cited by users.
```
@article{GPflow2020multioutput,
author = {{van der Wilk}, Mark and Dutordoir, Vincent and John, ST and
Artemev, Artem and Adam, Vincent and Hensman, James},
title = {A Framework for Interdomain and Multioutput {G}aussian Processes},
year = {2020},
journal = {arXiv:2003.01115},
url = {https://arxiv.org/abs/2003.01115}
}
```
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Matthews](https://github.com/alexggmatthews).\nIt is now actively maintained by (in alphabetical order)\n[Artem Artemev](http://github.com/awav/),\n[Mark van der Wilk](https://markvdw.github.io/),\n[ST John](https://github.com/st--),\nand [Vincent Dutordoir](https://vdutor.github.io/).\nGPflow would not be the same without the community. **We are grateful to [all contributors](CONTRIBUTORS.md) who have helped shape GPflow.**\n\n *GPflow is an open source project. If you have relevant skills and are interested in contributing then please do contact us (see [\"The GPflow community\" section](#the-gpflow-community) below).*\n\n\n## Installation\n\n### Requirements\n\nGPflow depends on both TensorFlow (TF, version \u2265 2.4) and TensorFlow Probability (TFP, version \u2265 0.12). We support Python \u2265 3.7.\n\n**NOTE:** TensorFlow Probability releases are tightly coupled to TensorFlow, e.g. TFP 0.14 requires TF>=2.6, TFP 0.13 requires TF>=2.5, and TFP 0.12 requires TF>=2.4. Unfortunately, this is _not_ specified in TFP's dependencies. So if you already have an (older) version of TensorFlow installed, GPflow will pull in the latest TFP, which will be incompatible. If you get errors such as `ImportError: This version of TensorFlow Probability requires TensorFlow version >= 2.4`, you have to either upgrade TensorFlow (`pip install -U tensorflow`) or manually install an older version of the `tensorflow_probability` package.\n\n### Latest (stable) release from PyPI\n\n```bash\npip install gpflow\n```\n\n### Latest (bleeding-edge) source from GitHub\n\n*Be aware that the `develop` branch may change regularly, and new commits may break your code.*\n\nIn a check-out of the `develop` branch of the [GPflow GitHub repository](https://github.com/GPflow/GPflow), run\n```bash\npip install -e .\n```\n\nAlternatively, you can install the latest GitHub `develop` version using `pip`:\n```bash\npip install git+https://github.com/GPflow/GPflow.git@develop#egg=gpflow\n```\nThis will automatically install all required dependencies.\n\n## Getting Started with GPflow 2.0\n\nThere is an [\"Intro to GPflow 2.0\"](https://gpflow.github.io/GPflow/develop/notebooks/intro_to_gpflow2.html) Jupyter notebook; check it out for details.\nTo convert your code from GPflow 1 check the [GPflow 2 upgrade guide](https://gpflow.github.io/GPflow/develop/notebooks/gpflow2_upgrade_guide.html).\n\n\n## The GPflow Community\n\n### Getting help\n\n**Bugs, feature requests, pain points, annoying design quirks, etc:**\nPlease use [GitHub issues](https://github.com/GPflow/GPflow/issues/) to flag up bugs/issues/pain points, suggest new features, and discuss anything else related to the use of GPflow that in some sense involves changing the GPflow code itself.\nYou can make use of the [labels](https://github.com/GPflow/GPflow/labels) such as [`bug`](https://github.com/GPflow/GPflow/labels/bug), [`discussion`](https://github.com/GPflow/GPflow/labels/discussion), [`feature`](https://github.com/GPflow/GPflow/labels/feature), [`feedback`](https://github.com/GPflow/GPflow/labels/feedback), etc.\nWe positively welcome comments or concerns about usability, and suggestions for changes at any level of design.\n\nWe aim to respond to issues promptly, but if you believe we may have forgotten about an issue, please feel free to add another comment to remind us.\n\n**\"How-to-use\" questions:**\nPlease use [Stack Overflow (gpflow tag)](https://stackoverflow.com/tags/gpflow) to ask questions that relate to \"how to use GPflow\", i.e. questions of understanding rather than issues that require changing GPflow code. (If you are unsure where to ask, you are always welcome to open a GitHub issue; we may then ask you to move your question to Stack Overflow.)\n\n### Slack workspace\n\nWe have a public [GPflow slack workspace](https://gpflow.slack.com/). Please use this [invite link](https://join.slack.com/t/gpflow/shared_invite/enQtOTE5MDA0Nzg5NjA2LTYwZWI3MzhjYjNlZWI1MWExYzZjMGNhOWIwZWMzMGY0YjVkYzAyYjQ4NjgzNDUyZTgyNzcwYjAyY2QzMWRmYjE) if you'd like to join, whether to ask short informal questions or to be involved in the discussion and future development of GPflow.\n\n### Contributing\n\nAll constructive input is gratefully received. For more information, see the [notes for contributors](CONTRIBUTING.md).\n\n### Projects using GPflow\n\nProjects building on GPflow and demonstrating its usage are listed below. The following projects are based on the current GPflow 2.x release:\n\n| Project | Description |\n| --- | --- |\n| [Trieste](https://github.com/secondmind-labs/trieste) | Bayesian optimization with TensorFlow, with out-of-the-box support for GPflow (2.x) models. |\n| [VFF](https://github.com/st--/VFF) | Variational Fourier Features for Gaussian Processes (GPflow 2.x version) |\n| [BranchedGP](https://github.com/ManchesterBioinference/BranchedGP) | Gaussian processes with branching kernels.|\n| [VBPP](https://github.com/st--/vbpp) | Implementation of \"Variational Bayes for Point Processes\".|\n| [Gaussian Process Regression on Molecules](https://medium.com/@ryangriff123/gaussian-process-regression-on-molecules-in-gpflow-ee6fedab2130) | GPs to predict molecular properties by creating a custom-defined Tanimoto kernel to operate on Morgan fingerprints |\n\nIf you would like your project listed here, let us know - or simply [open a pull request](https://github.com/GPflow/GPflow/compare) that adds your project to the table above!\n\n*The following projects build on older versions of GPflow (pre-2020); we encourage their authors to upgrade to GPflow 2.*\n\n| Project | Description |\n| --- | --- |\n| [GPflowOpt](https://github.com/GPflow/GPflowOpt) | Bayesian Optimization using GPflow (stable release requires GPflow 0.5). |\n| [Doubly-Stochastic-DGP](https://github.com/ICL-SML/Doubly-Stochastic-DGP)| Deep Gaussian Processes with Doubly Stochastic Variational Inference.|\n| [widedeepnetworks](https://github.com/widedeepnetworks/widedeepnetworks) | Measuring the relationship between random wide deep neural networks and GPs.|\n| [orth_decoupled_var_gps](https://github.com/hughsalimbeni/orth_decoupled_var_gps) | Variationally sparse GPs with orthogonally decoupled bases|\n| [kernel_learning](https://github.com/frgsimpson/kernel_learning) | Implementation of \"Differentiable Compositional Kernel Learning for Gaussian Processes\".|\n| [DGPs_with_IWVI](https://github.com/hughsalimbeni/DGPs_with_IWVI) | Deep Gaussian Processes with Importance-Weighted Variational Inference|\n| [kerndisc](https://github.com/BracketJohn/kernDisc) | Library for automated kernel structure discovery in univariate data|\n| [Signature covariances](https://github.com/tgcsaba/GPSig) | kernels for (time)series as *inputs* |\n| [Structured-DGP](https://github.com/boschresearch/Structured_DGP) | Adding more structure to the variational posterior of the Doubly Stochastic Deep Gaussian Process |\n\n## Version Compatibility\n\nGPflow heavily depends on TensorFlow and as far as TensorFlow supports forward compatibility, GPflow should as well. The version of GPflow can give you a hint about backward compatibility. If the major version has changed then you need to check the release notes to find out how the API has been changed.\n\nUnfortunately, there is no such thing as backward compatibility for GPflow _models_, which means that a model implementation can change without changing interfaces. In other words, the TensorFlow graph can be different for the same models from different versions of GPflow.\n\n### TensorFlow 1.x and GPflow 1.x\n\nWe have stopped development and support for GPflow based on TensorFlow 1.\nThe latest release supporting TensorFlow 1 is [v1.5.1](https://github.com/GPflow/GPflow/releases/tag/v1.5.1).\n[Documentation](https://gpflow.readthedocs.io/en/v1.5.1-docs/) and\n[tutorials](https://nbviewer.jupyter.org/github/GPflow/GPflow/blob/v1.5.1/doc/sphinx/notebooks/intro.ipynb)\nwill remain available.\n\n\n## Citing GPflow\n\nTo cite GPflow, please reference the [JMLR paper](http://www.jmlr.org/papers/volume18/16-537/16-537.pdf). Sample Bibtex is given below:\n```\n@ARTICLE{GPflow2017,\n author = {Matthews, Alexander G. de G. and {van der Wilk}, Mark and Nickson, Tom and\n\tFujii, Keisuke. and {Boukouvalas}, Alexis and {Le{\\'o}n-Villagr{\\'a}}, Pablo and\n\tGhahramani, Zoubin and Hensman, James},\n title = \"{{GP}flow: A {G}aussian process library using {T}ensor{F}low}\",\n journal = {Journal of Machine Learning Research},\n year = {2017},\n month = {apr},\n volume = {18},\n number = {40},\n pages = {1-6},\n url = {http://jmlr.org/papers/v18/16-537.html}\n}\n```\n\nSince the publication of the GPflow paper, the software has been significantly extended\nwith the framework for interdomain approximations and multioutput priors. We review the\nframework and describe the design in an [arXiv paper](https://arxiv.org/abs/2003.01115),\nwhich can be cited by users.\n```\n@article{GPflow2020multioutput,\n author = {{van der Wilk}, Mark and Dutordoir, Vincent and John, ST and\n Artemev, Artem and Adam, Vincent and Hensman, James},\n title = {A Framework for Interdomain and Multioutput {G}aussian Processes},\n year = {2020},\n journal = {arXiv:2003.01115},\n url = {https://arxiv.org/abs/2003.01115}\n}\n```\n",
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