aemcmc-nightly 0.0.7.dev20230119

Miscellaneous MCMC samplers written in Aesara

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"

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

p_posterior_step = sampler.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
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"

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

# `sampler.sample_steps` contains the sample step for each random variable
print(sampler.sample_steps[h_rv])
# h_posterior

# `sampler.stages` contains the sampling kernels sorted by scan order
print(sampler.stages)
# {HorseshoeGibbsKernel: [tau, lambda], NBRegressionGibbsKernel: [beta], DispersionGibbsKernel: [h]}

# Build a function that returns new samples
to_sample_rvs = [tau_rv, lmbda_rv, beta_rv, h_rv]
inputs = [a, b, X, y_vv] + [initial_values[rv] for rv in to_sample_rvs]
outputs = [sampler.sample_steps[rv] for rv in to_sample_rvs]
sample_fn = aesara.function(inputs, outputs, updates=sampler.updates)

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
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()

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

print(sampler.sample_steps.keys())
# dict_keys([sigma, mu])
print(sampler.stages)
# {NUTSKernel: [sigma, mu]}
print(sampler.parameters)
# {NUTSKernel: (step_size, inverse_mass_matrix)}

# Build a function that returns new samples
step_size, inverse_mass_matrix = list(sampler.parameters.values())[0]
inputs = [
    initial_values[mu_rv],
    initial_values[sigma_rv],
    y_vv,
    step_size,
    inverse_mass_matrix
]
outputs = [sampler.sample_steps[mu_rv], sampler.sample_steps[sigma_rv]]
sample_fn = aesara.function(inputs, outputs, updates=sampler.updates)

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