Automatically Marginalized MCMC in Probabilistic Programming

TL;DR

This paper introduces an automatic marginalization technique integrated with Hamiltonian Monte Carlo in probabilistic programming, simplifying complex models and enhancing sampling efficiency for hierarchical Bayesian models.

Contribution

It presents a novel method for automatic marginalization within HMC in PPLs, improving sampling performance on hierarchical models.

Findings

Significant improvement in sampling efficiency for hierarchical models

Automatic marginalization reduces the need for reparameterization tricks

Enhanced applicability of HMC in complex probabilistic models

Abstract

Hamiltonian Monte Carlo (HMC) is a powerful algorithm to sample latent variables from Bayesian models. The advent of probabilistic programming languages (PPLs) frees users from writing inference algorithms and lets users focus on modeling. However, many models are difficult for HMC to solve directly, and often require tricks like model reparameterization. We are motivated by the fact that many of those models could be simplified by marginalization. We propose to use automatic marginalization as part of the sampling process using HMC in a graphical model extracted from a PPL, which substantially improves sampling from real-world hierarchical models.