On the Partition Function and Random Maximum A-Posteriori Perturbations

TL;DR

This paper introduces a novel approach linking the partition function to max-statistics of random variables, enabling efficient approximation via MAP inference with perturbations, especially effective in complex energy landscapes.

Contribution

It presents a new framework for approximating the partition function using MAP inference on randomly perturbed models, leveraging efficient solvers like graph-cuts.

Findings

Effective in high signal-high coupling regimes

Outperforms alternative methods in complex energy landscapes

Utilizes efficient MAP solvers for partition function evaluation

Abstract

In this paper we relate the partition function to the max-statistics of random variables. In particular, we provide a novel framework for approximating and bounding the partition function using MAP inference on randomly perturbed models. As a result, we can use efficient MAP solvers such as graph-cuts to evaluate the corresponding partition function. We show that our method excels in the typical "high signal - high coupling" regime that results in ragged energy landscapes difficult for alternative approaches.