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The Inference Gym is the place to exercise inference methods to help make them faster, leaner and more robust.

Project description

Inference Gym


The Inference Gym is the place to exercise inference methods to help make them faster, leaner and more robust. The goal of the Inference Gym is to provide a set of probabilistic inference problems with a standardized interface, making it easy to test new inference techniques across a variety of challenging tasks.

Currently it provides a repository of probabilistic models that can be used to benchmark (the computational and statistical performance of) inference algorithms. Probabilistic models are implemented as subclasses of the Model class, which minimally provides the following faculties:

  • A description of the shapes and dtypes of the parameters of the model.
  • Event space bijectors which map from the unconstrained real space, to the support of the model's associated density.
  • Ability to compute the log un-normalized density at a certain parameter setting.
  • Name of the model.
  • Sample transformations, which when applied to samples from the model's density represent quantities with a useful interpretation.

Each model can additionally provide:

  • Ground truth quantities associated with each sample transformation. This can include mean, variance and other statistics. If these are estimated via Monte-Carlo methods, a standard error is also provided. This can be used to verify the algorithm's level of bias.

Getting started

Check out the tutorial.


pip install tfp-nightly inference_gym
# Install at least one the folowing
pip install tf-nightly  # For the TensorFlow backend.
pip install jax jaxlib  # For the JAX backend.
# Install to support external datasets
pip install tfds-nightly
import matplotlib.pyplot as plt
import numpy as np
from inference_gym import using_tensorflow as

model = inference_gym.targets.GermanCreditNumericLogisticRegression()

samples = inference_method(

plt.suptitle(str(model))  # 'German Credit Numeric Logistic Regression'
for i, (name, sample_transformation) in enumerate(
  transformed_samples = sample_transformation(samples)
  bias_sq = tf.square(
      tf.reduce_mean(transformed_samples, 0) -
  ess = compute_ess(  # E.g. tfp.mcmc.effective_sample_size if using MCMC.
  plt.subplot(len(model.sample_transformations), 2, 2 * i + 1)
  plt.title('{} bias^2'.format(sample_transformation))  # e.g. 'Identity bias^2'[-1]), bias_sq)
  plt.subplot(len(model.sample_transformations), 2, 2 * i + 2)
  plt.title('{} ess'.format(sample_transformation))[-1]), ess)

Also, see VectorModel which can be used to simplify the interface requirements for the inference method.

What makes for a good Inference Gym Model?

A good model should ideally do one or more of these:

  • Help build intuition (usually 1D or 2D for ease of visualization)
  • Represent a generally important application of Bayesian inference
  • Pose a challenge for inference, e.g.
    • high dimensionality
    • poor or pathological conditioning
    • mixing continuous and discrete latents
    • multimodality
    • non-identifiability
    • expensive gradients

Naturally, a model shouldn’t have all of those properties so users can more easily do experiments to tease out which complication has what effect on the inference procedure. This isn’t an exhaustive list.

Making changes

Adding a new model

It's easiest to mimic an existing example. Here's a small table to help you find an example. If your model isn't described well by these possibilities, feel free to ask for help.

Bayesian Model? Real dataset? Analytic Ground Truth? Stan Implementation? Multiple RVs? Example Model
Yes Real No Yes Yes GermanCreditNumericSparseLogicRegression
Yes Real No Yes No GermanCreditLogicRegression
Yes Synthetic No Yes Yes SyntheticItemResponseTheory
No None Yes No No IllConditionedGaussian

A Bayesian model in the table above refers to models whose density over the parameters is computed using the product of a prior and a likelihood function (i.e. using Bayes' theorem). These models should inherit from the BayesianModel class, as it provides some utilities for such models.

Currently we have a little tooling to help use cmdstanpy to generate ground truth values (in the correct format) for models without analytic ground truth. Using this requires adding a model implementation inside the inference_gym/tools/stan directory.

New (and existing) models should follow the Model Contract.

Adding a new real dataset

We strongly encourage you to add your dataset to TensorFlow Datasets first. Then, you can follow the example of the German Credit (numeric) dataset used in the GermanCreditLogicRegression.

Adding a new synthetic dataset

Follow the example of the SyntheticItemResponseTheory model.

Generating ground truth files.

See inference_gym/tools/

Citing Inference Gym

To cite the Inference Gym:

  author = {Pavel Sountsov and Alexey Radul and contributors},
  title = {Inference Gym},
  url = {},
  version = {0.0.4},
  year = {2020},

Make sure to update the version attribute to match the actual version you're using.

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