Accelerating Metropolis-Hastings with Lightweight Inference Compilation

TL;DR

This paper introduces Lightweight Inference Compilation (LIC), a novel approach combining probabilistic graphical models and neural networks to improve proposal distributions in Metropolis-Hastings sampling, enhancing efficiency and robustness.

Contribution

LIC is a new framework that uses graph neural networks within a declarative probabilistic programming language to directly optimize proposal distributions for MCMC, avoiding importance sampling of execution traces.

Findings

LIC produces simpler proposers with fewer parameters.

LIC demonstrates greater robustness to nuisance variables.

LIC improves posterior sampling accuracy in Bayesian logistic regression and n-schools inference.

Abstract

In order to construct accurate proposers for Metropolis-Hastings Markov Chain Monte Carlo, we integrate ideas from probabilistic graphical models and neural networks in an open-source framework we call Lightweight Inference Compilation (LIC). LIC implements amortized inference within an open-universe declarative probabilistic programming language (PPL). Graph neural networks are used to parameterize proposal distributions as functions of Markov blankets, which during "compilation" are optimized to approximate single-site Gibbs sampling distributions. Unlike prior work in inference compilation (IC), LIC forgoes importance sampling of linear execution traces in favor of operating directly on Bayesian networks. Through using a declarative PPL, the Markov blankets of nodes (which may be non-static) are queried at inference-time to produce proposers Experimental results show LIC can produce proposers which have less parameters, greater robustness to nuisance random variables, and improved posterior sampling in a Bayesian logistic regression and $n$-schools inference application.