Accelerating Metropolis-Hastings with Lightweight Inference Compilation
This work addresses the challenge of efficient inference in probabilistic programming for researchers and practitioners, though it appears incremental as it builds on prior inference compilation methods by operating directly on Bayesian networks instead of linear execution traces.
The paper tackles the problem of constructing accurate proposers for Metropolis-Hastings MCMC by integrating probabilistic graphical models and neural networks in a framework called Lightweight Inference Compilation (LIC), resulting in proposers with fewer parameters, greater robustness to nuisance variables, and improved posterior sampling in applications like Bayesian logistic regression and n-schools inference.
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.