Probabilistic modeling and statistical inference in TensorFlow
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.
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
in core TF.
Layer 1: Statistical Building Blocks
- Distributions (
tfp.distributions): A large collection of probability distributions and related statistics with batch and broadcasting semantics. See the Distributions Tutorial.
- Bijectors (
tfp.bijectors): Reversible and composable transformations of random variables. Bijectors provide a rich class of transformed distributions, from classical examples like the log-normal distribution to sophisticated deep learning models such as masked autoregressive flows.
Layer 2: Model Building
- Joint Distributions (e.g.,
tfp.distributions.JointDistributionSequential): Joint distributions over one or more possibly-interdependent distributions. For an introduction to modeling with TFP's
JointDistributions, check out this colab
- Probabilistic Layers (
tfp.layers): Neural network layers with uncertainty over the functions they represent, extending TensorFlow Layers.
Layer 3: Probabilistic Inference
- Markov chain Monte Carlo (
tfp.mcmc): Algorithms for approximating integrals via sampling. Includes Hamiltonian Monte Carlo, random-walk Metropolis-Hastings, and the ability to build custom transition kernels.
- Variational Inference (
tfp.vi): Algorithms for approximating integrals via optimization.
- Optimizers (
tfp.optimizer): Stochastic optimization methods, extending TensorFlow Optimizers. Includes Stochastic Gradient Langevin Dynamics.
- Monte Carlo (
tfp.monte_carlo): Tools for computing Monte Carlo expectations.
TensorFlow Probability is under active development. Interfaces may change at any time.
for end-to-end examples. It includes tutorial notebooks such as:
- Linear Mixed Effects Models. A hierarchical linear model for sharing statistical strength across examples.
- Eight Schools. A hierarchical normal model for exchangeable treatment effects.
- Hierarchical Linear Models. Hierarchical linear models compared among TensorFlow Probability, R, and Stan.
- Bayesian Gaussian Mixture Models. Clustering with a probabilistic generative model.
- Probabilistic Principal Components Analysis. Dimensionality reduction with latent variables.
- Gaussian Copulas. Probability distributions for capturing dependence across random variables.
- TensorFlow Distributions: A Gentle Introduction. Introduction to TensorFlow Distributions.
- Understanding TensorFlow Distributions Shapes. How to distinguish between samples, batches, and events for arbitrarily shaped probabilistic computations.
- TensorFlow Probability Case Study: Covariance Estimation. A user's case study in applying TensorFlow Probability to estimate covariances.
It also includes example scripts such as:
- Variational Autoencoders. Representation learning with a latent code and variational inference.
- Vector-Quantized Autoencoder. Discrete representation learning with vector quantization.
- Disentangled Sequential Variational Autoencoder Disentangled representation learning over sequences with variational inference.
- Grammar Variational Autoencoder. Representation learning over productions in a context-free grammar.
- Latent Dirichlet Allocation (Distributions version, Mixed membership modeling for capturing topics in a document.
- Deep Exponential Family. A deep, sparse generative model for discovering a hierarchy of topics.
- Bayesian Neural Networks. Neural networks with uncertainty over their weights.
- Bayesian Logistic Regression. Bayesian inference for binary classification.
For additional details on installing TensorFlow, guidance installing prerequisites, and (optionally) setting up virtual environments, see the TensorFlow installation guide.
To install the latest stable version, run the following:
# 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
To use a pre-2.0 version of TensorFlow, run:
python -m pip install --upgrade --user "tensorflow<2" "tensorflow_probability<0.9"
Note: Since TensorFlow is not included
as a dependency of the TensorFlow Probability package (in
setup.py), you must
explicitly install the TensorFlow package (
This allows us to maintain one package instead of separate packages for CPU and
GPU-enabled TensorFlow. See the
TFP release notes for more
details about dependencies between TensorFlow and TensorFlow Probability.
There are also nightly builds of TensorFlow Probability under the pip package
tfp-nightly, which depends on one of
Nightly builds include newer features, but may be less stable than the
versioned releases. Both stable and nightly docs are available
python -m pip install --upgrade --user tf-nightly tfp-nightly
Installing from Source
You can also install from source. This requires the Bazel build system. It is highly recommended that you install
the nightly build of TensorFlow (
tf-nightly) before trying to build
TensorFlow Probability from source.
# 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
As part of TensorFlow, we're committed to fostering an open and welcoming environment.
- Stack Overflow: Ask or answer technical questions.
- GitHub: Report bugs or make feature requests.
- TensorFlow Blog: Stay up to date on content from the TensorFlow team and best articles from the community.
- Youtube Channel: Follow TensorFlow shows.
- email@example.com: Open mailing list for discussion and questions.
See the TensorFlow Community page for more details. Check out our latest publicity here:
- Coffee with a Googler: Probabilistic Machine Learning in TensorFlow
- Introducing TensorFlow Probability
We're eager to collaborate with you! See
for a guide on how to contribute. This project adheres to TensorFlow's
code of conduct. By participating, you are expected to
uphold this code.
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.
(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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