Skip to main content

Miscellaneous MCMC samplers written in Aesara

Project description

Tests Status Coverage Gitter

AeMCMC is a Python library that automates the construction of samplers for Aesara graphs that represent statistical models.

Features

This project is currently in an alpha state, but the basic features/objectives are currently as follows:

  • Provide utilities that simplify the process of constructing Aesara graphs/functions for posterior and posterior predictive sampling

  • Host a wide array of “exact” posterior sampling steps (e.g. Gibbs steps, scale-mixture/decomposition-based conditional samplers, etc.)

  • Build a framework for identifying and composing said sampler steps and enumerating the possible samplers for an arbitrary model

Overall, we would like this project to serve as a hub for community-sourced specialized samplers and facilitate their general use.

Getting started

Using AeMCMC, one can construct sampling steps from a graph containing Aesara RandomVariables. AeMCMC analyzes the model graph and possibly rewrites it to find the most suitable sampler.

AeMCMC can recognize closed-form posteriors; for instance the following Beta-Binomial model amounts to sampling from a Beta distribution:

import aesara
import aemcmc
import aesara.tensor as at

srng = at.random.RandomStream(0)

p_rv = srng.beta(1., 1., name="p")
Y_rv = srng.binomial(10, p_rv, name="Y")

y_vv = Y_rv.clone()
y_vv.name = "y"

sample_steps, _, initial_values, _ = aemcmc.construct_sampler(
    {Y_rv: y_vv}, srng
)

p_posterior_step = sample_steps[p_rv]
aesara.dprint(p_posterior_step)
# beta_rv{0, (0, 0), floatX, False}.1 [id A]
#  |RandomGeneratorSharedVariable(<Generator(PCG64) at 0x7F77B2831200>) [id B]
#  |TensorConstant{[]} [id C]
#  |TensorConstant{11} [id D]
#  |Elemwise{add,no_inplace} [id E]
#  | |TensorConstant{1.0} [id F]
#  | |y [id G]
#  |Elemwise{sub,no_inplace} [id H]
#    |Elemwise{add,no_inplace} [id I]
#    | |TensorConstant{1.0} [id F]
#    | |TensorConstant{10} [id J]
#    |y [id G]

sample_fn = aesara.function([y_vv], p_posterior_step)

AeMCMC also contains a database of Gibbs samplers that can be used to sample some models more efficiently than a general-purpose sampler like NUTS would:

import aemcmc
import aesara.tensor as at

srng = at.random.RandomStream(0)

X = at.matrix("X")

# Horseshoe prior for `beta_rv`
tau_rv = srng.halfcauchy(0, 1, name="tau")
lmbda_rv = srng.halfcauchy(0, 1, size=X.shape[1], name="lambda")
beta_rv = srng.normal(0, lmbda_rv * tau_rv, size=X.shape[1], name="beta")

a = at.scalar("a")
b = at.scalar("b")
h_rv = srng.gamma(a, b, name="h")

# Negative-binomial regression
eta = X @ beta_rv
p = at.sigmoid(-eta)
Y_rv = srng.nbinom(h_rv, p, name="Y")

y_vv = Y_rv.clone()
y_vv.name = "y"

sample_steps, updates, initial_values, parameters = aemcmc.construct_sampler(
    {Y_rv: y_vv}, srng
)
print(sample_steps.keys())
# dict_keys([tau, lambda, beta, h])

In case no specialized sampler is found, AeMCMC assigns the NUTS sampler to the remaining variables. AeMCMC reparametrizes the model automatically to improve sampling if needed:

import aemcmc
import aesara.tensor as at

srng = at.random.RandomStream(0)
mu_rv = srng.normal(0, 1, name="mu")
sigma_rv = srng.halfnormal(0.0, 1.0, name="sigma")
Y_rv = srng.normal(mu_rv, sigma_rv, name="Y")

y_vv = Y_rv.clone()

sample_steps, updates, initial_values, parameters = aemcmc.construct_sampler(
    {Y_rv: y_vv}, srng
)
print(sample_steps.keys())
# dict_keys([sigma, mu])
print(parameters.keys())
# dict_keys(['step_size', 'inverse_mass_matrix'])

Installation

The latest release of AeMCMC can be installed from PyPI using pip:

pip install aemcmc

Or via conda-forge:

conda install -c conda-forge aemcmc

The current development branch of AeMCMC can be installed from GitHub, also using pip:

pip install git+https://github.com/aesara-devs/aemcmc

Project details


Release history Release notifications | RSS feed

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distributions

No source distribution files available for this release.See tutorial on generating distribution archives.

Built Distribution

aemcmc_nightly-0.0.6-py3-none-any.whl (25.6 kB view hashes)

Uploaded Python 3

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page