On Sampling from the Gibbs Distribution with Random Maximum A-Posteriori Perturbations

TL;DR

This paper introduces a novel method that uses MAP inference with low-dimensional perturbations to efficiently sample from Gibbs distributions and derive lower bounds on partition functions, especially effective in complex energy landscapes.

Contribution

It presents a new approach combining MAP inference and perturbations for sampling from Gibbs distributions, offering improved efficiency and bounds in challenging scenarios.

Findings

Method performs well in high signal-high coupling regimes.

Provides both approximate and unbiased sampling techniques.

Outperforms existing methods in complex energy landscapes.

Abstract

In this paper we describe how MAP inference can be used to sample efficiently from Gibbs distributions. Specifically, we provide means for drawing either approximate or unbiased samples from Gibbs' distributions by introducing low dimensional perturbations and solving the corresponding MAP assignments. Our approach also leads to new ways to derive lower bounds on partition functions. We demonstrate empirically that our method excels in the typical "high signal - high coupling" regime. The setting results in ragged energy landscapes that are challenging for alternative approaches to sampling and/or lower bounds.