Output-Sensitive Adaptive Metropolis-Hastings for Probabilistic Programs

TL;DR

This paper presents AdLMH, an adaptive Metropolis-Hastings algorithm for probabilistic programs that improves convergence by adjusting proposal probabilities, demonstrating consistent performance gains over existing methods.

Contribution

The paper introduces AdLMH, a novel adaptive algorithm that enhances Lightweight Metropolis-Hastings for probabilistic programming, ensuring convergence and improved efficiency.

Findings

AdLMH converges to the correct distribution.

AdLMH shows improved convergence over LMH in tests.

The adaptation scheme enhances sampling efficiency.

Abstract

We introduce an adaptive output-sensitive Metropolis-Hastings algorithm for probabilistic models expressed as programs, Adaptive Lightweight Metropolis-Hastings (AdLMH). The algorithm extends Lightweight Metropolis-Hastings (LMH) by adjusting the probabilities of proposing random variables for modification to improve convergence of the program output. We show that AdLMH converges to the correct equilibrium distribution and compare convergence of AdLMH to that of LMH on several test problems to highlight different aspects of the adaptation scheme. We observe consistent improvement in convergence on the test problems.