# TensorFlow Probability
TensorFlow Probability is a library for probabilistic reasoning and statistical
analysis in TensorFlow. As part of the TensorFlow ecosystem, TensorFlow
Probability provides integration of probabilistic methods with deep networks,
gradient-based inference via automatic differentiation, and scalability to
large datasets and models via hardware acceleration (e.g., GPUs) and distributed
computation.
__TFP also works as "Tensor-friendly Probability" in pure JAX!__:
`from tensorflow_probability.substrates import jax as tfp` --
Learn more [here](https://www.tensorflow.org/probability/examples/TensorFlow_Probability_on_JAX).
Our probabilistic machine learning tools are structured as follows.
__Layer 0: TensorFlow.__ Numerical operations. In particular, the LinearOperator
class enables matrix-free implementations that can exploit special structure
(diagonal, low-rank, etc.) for efficient computation. It is built and maintained
by the TensorFlow Probability team and is now part of
[`tf.linalg`](https://github.com/tensorflow/tensorflow/tree/master/tensorflow/python/ops/linalg)
in core TF.
__Layer 1: Statistical Building Blocks__
* Distributions ([`tfp.distributions`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/python/distributions)):
A large collection of probability
distributions and related statistics with batch and
[broadcasting](https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
semantics. See the
[Distributions Tutorial](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/TensorFlow_Distributions_Tutorial.ipynb).
* Bijectors ([`tfp.bijectors`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/python/bijectors)):
Reversible and composable transformations of random variables. Bijectors
provide a rich class of transformed distributions, from classical examples
like the
[log-normal distribution](https://en.wikipedia.org/wiki/Log-normal_distribution)
to sophisticated deep learning models such as
[masked autoregressive flows](https://arxiv.org/abs/1705.07057).
__Layer 2: Model Building__
* Joint Distributions (e.g., [`tfp.distributions.JointDistributionSequential`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/python/distributions/joint_distribution_sequential.py)):
Joint distributions over one or more possibly-interdependent distributions.
For an introduction to modeling with TFP's `JointDistribution`s, check out
[this colab](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Modeling_with_JointDistribution.ipynb)
* Probabilistic Layers ([`tfp.layers`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/python/layers)):
Neural network layers with uncertainty over the functions they represent,
extending TensorFlow Layers.
__Layer 3: Probabilistic Inference__
* Markov chain Monte Carlo ([`tfp.mcmc`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/python/mcmc)):
Algorithms for approximating integrals via sampling. Includes
[Hamiltonian Monte Carlo](https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo),
random-walk Metropolis-Hastings, and the ability to build custom transition
kernels.
* Variational Inference ([`tfp.vi`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/python/vi)):
Algorithms for approximating integrals via optimization.
* Optimizers ([`tfp.optimizer`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/python/optimizer)):
Stochastic optimization methods, extending TensorFlow Optimizers. Includes
[Stochastic Gradient Langevin Dynamics](http://www.icml-2011.org/papers/398_icmlpaper.pdf).
* Monte Carlo ([`tfp.monte_carlo`](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/python/monte_carlo)):
Tools for computing Monte Carlo expectations.
TensorFlow Probability is under active development. Interfaces may change at any
time.
## Examples
See [`tensorflow_probability/examples/`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/examples/)
for end-to-end examples. It includes tutorial notebooks such as:
* [Linear Mixed Effects Models](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Linear_Mixed_Effects_Models.ipynb).
A hierarchical linear model for sharing statistical strength across examples.
* [Eight Schools](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Eight_Schools.ipynb).
A hierarchical normal model for exchangeable treatment effects.
* [Hierarchical Linear Models](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/HLM_TFP_R_Stan.ipynb).
Hierarchical linear models compared among TensorFlow Probability, R, and Stan.
* [Bayesian Gaussian Mixture Models](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Bayesian_Gaussian_Mixture_Model.ipynb).
Clustering with a probabilistic generative model.
* [Probabilistic Principal Components Analysis](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Probabilistic_PCA.ipynb).
Dimensionality reduction with latent variables.
* [Gaussian Copulas](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Gaussian_Copula.ipynb).
Probability distributions for capturing dependence across random variables.
* [TensorFlow Distributions: A Gentle Introduction](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/TensorFlow_Distributions_Tutorial.ipynb).
Introduction to TensorFlow Distributions.
* [Understanding TensorFlow Distributions Shapes](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Understanding_TensorFlow_Distributions_Shapes.ipynb).
How to distinguish between samples, batches, and events for arbitrarily shaped
probabilistic computations.
* [TensorFlow Probability Case Study: Covariance Estimation](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/TensorFlow_Probability_Case_Study_Covariance_Estimation.ipynb).
A user's case study in applying TensorFlow Probability to estimate covariances.
It also includes example scripts such as:
Representation learning with a latent code and variational inference.
* [Vector-Quantized Autoencoder](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/examples/vq_vae.py).
Discrete representation learning with vector quantization.
* [Disentangled Sequential Variational Autoencoder](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/examples/disentangled_vae.py)
Disentangled representation learning over sequences with variational inference.
* [Bayesian Neural Networks](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/examples/bayesian_neural_network.py).
Neural networks with uncertainty over their weights.
* [Bayesian Logistic Regression](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/examples/logistic_regression.py).
Bayesian inference for binary classification.
## Installation
For additional details on installing TensorFlow, guidance installing
prerequisites, and (optionally) setting up virtual environments, see the
[TensorFlow installation guide](https://www.tensorflow.org/install).
### Stable Builds
To install the latest stable version, run the following:
```shell
# Notes:
# - The `--upgrade` flag ensures you'll get the latest version.
# - The `--user` flag ensures the packages are installed to your user directory
# rather than the system directory.
# - TensorFlow 2 packages require a pip >= 19.0
python -m pip install --upgrade --user pip
python -m pip install --upgrade --user tensorflow tensorflow_probability
```
For CPU-only usage (and a smaller install), install with `tensorflow-cpu`.
To use a pre-2.0 version of TensorFlow, run:
```shell
python -m pip install --upgrade --user "tensorflow<2" "tensorflow_probability<0.9"
```
Note: Since [TensorFlow](https://www.tensorflow.org/install) is *not* included
as a dependency of the TensorFlow Probability package (in `setup.py`), you must
explicitly install the TensorFlow package (`tensorflow` or `tensorflow-cpu`).
This allows us to maintain one package instead of separate packages for CPU and
GPU-enabled TensorFlow. See the
[TFP release notes](https://github.com/tensorflow/probability/releases) for more
details about dependencies between TensorFlow and TensorFlow Probability.
### Nightly Builds
There are also nightly builds of TensorFlow Probability under the pip package
`tfp-nightly`, which depends on one of `tf-nightly` or `tf-nightly-cpu`.
Nightly builds include newer features, but may be less stable than the
versioned releases. Both stable and nightly docs are available
[here](https://www.tensorflow.org/probability/api_docs/python/tfp?version=nightly).
```shell
python -m pip install --upgrade --user tf-nightly tfp-nightly
```
### Installing from Source
You can also install from source. This requires the [Bazel](
https://bazel.build/) build system. It is highly recommended that you install
the nightly build of TensorFlow (`tf-nightly`) before trying to build
TensorFlow Probability from source. The most recent version of Bazel that TFP
currently supports is 6.4.0; support for 7.0.0+ is WIP.
```shell
# sudo apt-get install bazel git python-pip # Ubuntu; others, see above links.
python -m pip install --upgrade --user tf-nightly
git clone https://github.com/tensorflow/probability.git
cd probability
bazel build --copt=-O3 --copt=-march=native :pip_pkg
PKGDIR=$(mktemp -d)
./bazel-bin/pip_pkg $PKGDIR
python -m pip install --upgrade --user $PKGDIR/*.whl
```
## Community
As part of TensorFlow, we're committed to fostering an open and welcoming
environment.
* [Stack Overflow](https://stackoverflow.com/questions/tagged/tensorflow): Ask
or answer technical questions.
* [GitHub](https://github.com/tensorflow/probability/issues): Report bugs or
make feature requests.
* [TensorFlow Blog](https://blog.tensorflow.org/): Stay up to date on content
from the TensorFlow team and best articles from the community.
* [Youtube Channel](http://youtube.com/tensorflow/): Follow TensorFlow shows.
* [tfprobability@tensorflow.org](https://groups.google.com/a/tensorflow.org/forum/#!forum/tfprobability):
Open mailing list for discussion and questions.
See the [TensorFlow Community](https://www.tensorflow.org/community/) page for
more details. Check out our latest publicity here:
+ [Coffee with a Googler: Probabilistic Machine Learning in TensorFlow](
https://www.youtube.com/watch?v=BjUkL8DFH5Q)
+ [Introducing TensorFlow Probability](
https://medium.com/tensorflow/introducing-tensorflow-probability-dca4c304e245)
## Contributing
We're eager to collaborate with you! See [`CONTRIBUTING.md`](CONTRIBUTING.md)
for a guide on how to contribute. This project adheres to TensorFlow's
[code of conduct](CODE_OF_CONDUCT.md). By participating, you are expected to
uphold this code.
## References
If you use TensorFlow Probability in a paper, please cite:
+ _TensorFlow Distributions._ Joshua V. Dillon, Ian Langmore, Dustin Tran,
Eugene Brevdo, Srinivas Vasudevan, Dave Moore, Brian Patton, Alex Alemi, Matt
Hoffman, Rif A. Saurous.
[arXiv preprint arXiv:1711.10604, 2017](https://arxiv.org/abs/1711.10604).
(We're aware there's a lot more to TensorFlow Probability than Distributions, but the Distributions paper lays out our vision and is a fine thing to cite for now.)
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"description": "# TensorFlow Probability\n\nTensorFlow Probability is a library for probabilistic reasoning and statistical\nanalysis in TensorFlow. As part of the TensorFlow ecosystem, TensorFlow\nProbability provides integration of probabilistic methods with deep networks,\ngradient-based inference via automatic differentiation, and scalability to\nlarge datasets and models via hardware acceleration (e.g., GPUs) and distributed\ncomputation.\n\n__TFP also works as \"Tensor-friendly Probability\" in pure JAX!__:\n`from tensorflow_probability.substrates import jax as tfp` --\nLearn more [here](https://www.tensorflow.org/probability/examples/TensorFlow_Probability_on_JAX).\n\nOur probabilistic machine learning tools are structured as follows.\n\n__Layer 0: TensorFlow.__ Numerical operations. In particular, the LinearOperator\nclass enables matrix-free implementations that can exploit special structure\n(diagonal, low-rank, etc.) for efficient computation. It is built and maintained\nby the TensorFlow Probability team and is now part of\n[`tf.linalg`](https://github.com/tensorflow/tensorflow/tree/master/tensorflow/python/ops/linalg)\nin core TF.\n\n__Layer 1: Statistical Building Blocks__\n\n* Distributions ([`tfp.distributions`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/python/distributions)):\n A large collection of probability\n distributions and related statistics with batch and\n [broadcasting](https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)\n semantics. See the\n [Distributions Tutorial](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/TensorFlow_Distributions_Tutorial.ipynb).\n* Bijectors ([`tfp.bijectors`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/python/bijectors)):\n Reversible and composable transformations of random variables. Bijectors\n provide a rich class of transformed distributions, from classical examples\n like the\n [log-normal distribution](https://en.wikipedia.org/wiki/Log-normal_distribution)\n to sophisticated deep learning models such as\n [masked autoregressive flows](https://arxiv.org/abs/1705.07057).\n\n__Layer 2: Model Building__\n\n* Joint Distributions (e.g., [`tfp.distributions.JointDistributionSequential`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/python/distributions/joint_distribution_sequential.py)):\n Joint distributions over one or more possibly-interdependent distributions.\n For an introduction to modeling with TFP's `JointDistribution`s, check out\n [this colab](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Modeling_with_JointDistribution.ipynb)\n* Probabilistic Layers ([`tfp.layers`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/python/layers)):\n Neural network layers with uncertainty over the functions they represent,\n extending TensorFlow Layers.\n\n__Layer 3: Probabilistic Inference__\n\n* Markov chain Monte Carlo ([`tfp.mcmc`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/python/mcmc)):\n Algorithms for approximating integrals via sampling. Includes\n [Hamiltonian Monte Carlo](https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo),\n random-walk Metropolis-Hastings, and the ability to build custom transition\n kernels.\n* Variational Inference ([`tfp.vi`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/python/vi)):\n Algorithms for approximating integrals via optimization.\n* Optimizers ([`tfp.optimizer`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/python/optimizer)):\n Stochastic optimization methods, extending TensorFlow Optimizers. Includes\n [Stochastic Gradient Langevin Dynamics](http://www.icml-2011.org/papers/398_icmlpaper.pdf).\n* Monte Carlo ([`tfp.monte_carlo`](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/python/monte_carlo)):\n Tools for computing Monte Carlo expectations.\n\nTensorFlow Probability is under active development. Interfaces may change at any\ntime.\n\n## Examples\n\nSee [`tensorflow_probability/examples/`](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/examples/)\nfor end-to-end examples. It includes tutorial notebooks such as:\n\n* [Linear Mixed Effects Models](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Linear_Mixed_Effects_Models.ipynb).\n A hierarchical linear model for sharing statistical strength across examples.\n* [Eight Schools](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Eight_Schools.ipynb).\n A hierarchical normal model for exchangeable treatment effects.\n* [Hierarchical Linear Models](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/HLM_TFP_R_Stan.ipynb).\n Hierarchical linear models compared among TensorFlow Probability, R, and Stan.\n* [Bayesian Gaussian Mixture Models](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Bayesian_Gaussian_Mixture_Model.ipynb).\n Clustering with a probabilistic generative model.\n* [Probabilistic Principal Components Analysis](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Probabilistic_PCA.ipynb).\n Dimensionality reduction with latent variables.\n* [Gaussian Copulas](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Gaussian_Copula.ipynb).\n Probability distributions for capturing dependence across random variables.\n* [TensorFlow Distributions: A Gentle Introduction](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/TensorFlow_Distributions_Tutorial.ipynb).\n Introduction to TensorFlow Distributions.\n* [Understanding TensorFlow Distributions Shapes](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Understanding_TensorFlow_Distributions_Shapes.ipynb).\n How to distinguish between samples, batches, and events for arbitrarily shaped\n probabilistic computations.\n* [TensorFlow Probability Case Study: Covariance Estimation](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/TensorFlow_Probability_Case_Study_Covariance_Estimation.ipynb).\n A user's case study in applying TensorFlow Probability to estimate covariances.\n\nIt also includes example scripts such as:\n\n Representation learning with a latent code and variational inference.\n* [Vector-Quantized Autoencoder](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/examples/vq_vae.py).\n Discrete representation learning with vector quantization.\n* [Disentangled Sequential Variational Autoencoder](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/examples/disentangled_vae.py)\n Disentangled representation learning over sequences with variational inference.\n* [Bayesian Neural Networks](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/examples/bayesian_neural_network.py).\n Neural networks with uncertainty over their weights.\n* [Bayesian Logistic Regression](https://github.com/tensorflow/probability/tree/main/tensorflow_probability/examples/logistic_regression.py).\n Bayesian inference for binary classification.\n\n## Installation\n\nFor additional details on installing TensorFlow, guidance installing\nprerequisites, and (optionally) setting up virtual environments, see the\n[TensorFlow installation guide](https://www.tensorflow.org/install).\n\n### Stable Builds\n\nTo install the latest stable version, run the following:\n\n```shell\n# Notes:\n\n# - The `--upgrade` flag ensures you'll get the latest version.\n# - The `--user` flag ensures the packages are installed to your user directory\n# rather than the system directory.\n# - TensorFlow 2 packages require a pip >= 19.0\npython -m pip install --upgrade --user pip\npython -m pip install --upgrade --user tensorflow tensorflow_probability\n```\n\nFor CPU-only usage (and a smaller install), install with `tensorflow-cpu`.\n\nTo use a pre-2.0 version of TensorFlow, run:\n\n```shell\npython -m pip install --upgrade --user \"tensorflow<2\" \"tensorflow_probability<0.9\"\n```\n\nNote: Since [TensorFlow](https://www.tensorflow.org/install) is *not* included\nas a dependency of the TensorFlow Probability package (in `setup.py`), you must\nexplicitly install the TensorFlow package (`tensorflow` or `tensorflow-cpu`).\nThis allows us to maintain one package instead of separate packages for CPU and\nGPU-enabled TensorFlow. See the\n[TFP release notes](https://github.com/tensorflow/probability/releases) for more\ndetails about dependencies between TensorFlow and TensorFlow Probability.\n\n\n### Nightly Builds\n\nThere are also nightly builds of TensorFlow Probability under the pip package\n`tfp-nightly`, which depends on one of `tf-nightly` or `tf-nightly-cpu`.\nNightly builds include newer features, but may be less stable than the\nversioned releases. Both stable and nightly docs are available\n[here](https://www.tensorflow.org/probability/api_docs/python/tfp?version=nightly).\n\n```shell\npython -m pip install --upgrade --user tf-nightly tfp-nightly\n```\n\n### Installing from Source\n\nYou can also install from source. This requires the [Bazel](\nhttps://bazel.build/) build system. It is highly recommended that you install\nthe nightly build of TensorFlow (`tf-nightly`) before trying to build\nTensorFlow Probability from source. The most recent version of Bazel that TFP\ncurrently supports is 6.4.0; support for 7.0.0+ is WIP.\n\n```shell\n# sudo apt-get install bazel git python-pip # Ubuntu; others, see above links.\npython -m pip install --upgrade --user tf-nightly\ngit clone https://github.com/tensorflow/probability.git\ncd probability\nbazel build --copt=-O3 --copt=-march=native :pip_pkg\nPKGDIR=$(mktemp -d)\n./bazel-bin/pip_pkg $PKGDIR\npython -m pip install --upgrade --user $PKGDIR/*.whl\n```\n\n## Community\n\nAs part of TensorFlow, we're committed to fostering an open and welcoming\nenvironment.\n\n* [Stack Overflow](https://stackoverflow.com/questions/tagged/tensorflow): Ask\n or answer technical questions.\n* [GitHub](https://github.com/tensorflow/probability/issues): Report bugs or\n make feature requests.\n* [TensorFlow Blog](https://blog.tensorflow.org/): Stay up to date on content\n from the TensorFlow team and best articles from the community.\n* [Youtube Channel](http://youtube.com/tensorflow/): Follow TensorFlow shows.\n* [tfprobability@tensorflow.org](https://groups.google.com/a/tensorflow.org/forum/#!forum/tfprobability):\n Open mailing list for discussion and questions.\n\nSee the [TensorFlow Community](https://www.tensorflow.org/community/) page for\nmore details. Check out our latest publicity here:\n\n+ [Coffee with a Googler: Probabilistic Machine Learning in TensorFlow](\n https://www.youtube.com/watch?v=BjUkL8DFH5Q)\n+ [Introducing TensorFlow Probability](\n https://medium.com/tensorflow/introducing-tensorflow-probability-dca4c304e245)\n\n## Contributing\n\nWe're eager to collaborate with you! See [`CONTRIBUTING.md`](CONTRIBUTING.md)\nfor a guide on how to contribute. This project adheres to TensorFlow's\n[code of conduct](CODE_OF_CONDUCT.md). By participating, you are expected to\nuphold this code.\n\n## References\n\nIf you use TensorFlow Probability in a paper, please cite:\n\n+ _TensorFlow Distributions._ Joshua V. Dillon, Ian Langmore, Dustin Tran,\nEugene Brevdo, Srinivas Vasudevan, Dave Moore, Brian Patton, Alex Alemi, Matt\nHoffman, Rif A. Saurous.\n[arXiv preprint arXiv:1711.10604, 2017](https://arxiv.org/abs/1711.10604).\n\n(We're aware there's a lot more to TensorFlow Probability than Distributions, but the Distributions paper lays out our vision and is a fine thing to cite for now.)\n",
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