Accelerating Metropolis-Hastings with Lightweight Inference Compilation
Feynman Liang, Nimar Arora, Nazanin Tehrani, Yucen Li, Michael Tingley, Erik Meijer
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.
BibTeX
@InProceedings{pmlr-v130-liang21a,
title = { Accelerating Metropolis-Hastings with Lightweight Inference Compilation },
author = {Liang, Feynman and Arora, Nimar and Tehrani, Nazanin and Li, Yucen and Tingley, Michael and Meijer, Erik},
booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics},
pages = {181--189},
year = {2021},
editor = {Banerjee, Arindam and Fukumizu, Kenji},
volume = {130},
series = {Proceedings of Machine Learning Research},
month = {13--15 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v130/liang21a/liang21a.pdf},
url = {https://proceedings.mlr.press/v130/liang21a.html},
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. }
}