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Pyro PPL on Numpy

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Probabilistic programming with NumPy powered by JAX for autograd and JIT compilation to GPU/CPU.

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What is NumPyro?

NumPyro is a small probabilistic programming library built on JAX. It essentially provides a NumPy backend for Pyro, with some minor changes to the inference API and syntax. Since we use JAX, we get autograd and JIT compilation to GPU / CPU for free. This is an alpha release under active development, so beware of brittleness, bugs, and changes to the API as the design evolves.

NumPyro is designed to be lightweight and focuses on providing a flexible substrate that users can build on:

  • Pyro Primitives: NumPyro programs can contain regular Python and NumPy code, in addition to Pyro primitives like sample and param. The model code should look very similar to Pyro except for some minor differences between PyTorch and Numpy's API. See Examples.
  • Inference algorithms: NumPyro currently supports Hamiltonian Monte Carlo, including an implementation of the No U-Turn Sampler. One of the motivations for NumPyro was to speed up Hamiltonian Monte Carlo by JIT compiling the verlet integration step that includes multiple gradient computations. With JAX, we can compose jit and grad to compile the entire integration step into an XLA optimized kernel. We also eliminate Python overhead by JIT compiling the entire tree building stage in NUTS (this is possible using Iterative NUTS). There is also a basic Variational Inference implementation for reparameterized distributions.
  • Distributions: The numpyro.distributions module provides distribution classes, constraints and bijective transforms. The distribution classes wrap over samplers implemented to work with JAX's functional pseudo-random number generator. The design of the distributions module largely follows from PyTorch. A major subset of the API is implemented, and it contains most of the common distributions that exist in PyTorch. As a result, Pyro and PyTorch users can rely on the same API and batching semantics as in torch.distributions. In addition to distributions, constraints and transforms are very useful when operating on distribution classes with bounded support.
  • Effect handlers: Like Pyro, primitives like sample and param can be interpreted with side-effects using effect-handlers from the numpyro.handlers module, and these can be easily extended to implement custom inference algorithms and inference utilities.


Limited Windows Support: Note that NumPyro is untested on Windows, and will require building jaxlib from source. See this JAX issue for more details.

To install NumPyro with a CPU version of JAX, you can use pip:

pip install numpyro

To use NumPyro on the GPU, you will need to first install jax and jaxlib with CUDA support.

You can also install NumPyro from source:

git clone
# install jax/jaxlib first for CUDA support
pip install -e .[dev]


For some examples on specifying models and doing inference in NumPyro:

Users will note that the API for model specification is largely the same as Pyro including the distributions API, by design. The interface for inference algorithms and other utility functions might deviate from Pyro in favor of a more functional style that works better with JAX. e.g. there is no global parameter store or random state.

Future Work

In the near term, we plan to work on the following. Please open new issues for feature requests and enhancements:

  • Improving robustness of inference on different models, profiling and performance tuning.
  • More inference algorithms, particularly those that require second order derivaties or use HMC.
  • Integration with Funsor to support inference algorithms with delayed sampling.
  • Supporting more distributions, extending the distributions API, and adding more samplers to JAX.
  • Other areas motivated by Pyro's research goals and application focus, and interest from the community.

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