Partition Function Estimation: A Quantitative Study

TL;DR

This paper surveys 18 techniques for estimating the partition function in probabilistic graphical models, revealing that exact methods are as efficient as approximate ones and highlighting opportunities for scalable approximate algorithms.

Contribution

It provides a comprehensive empirical comparison of existing partition function estimation methods and offers insights into their efficiency and potential for scalable approximate solutions.

Findings

Exact and approximate techniques have similar efficiency.

Significant performance gap between the Virtual Best Solver and top tools.

Opportunities exist for developing scalable approximate methods.

Abstract

Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its computation is key to several probabilistic reasoning tasks. Given the #P-hardness of computing the partition function, several techniques have been proposed over the years with varying guarantees on the quality of estimates and their runtime behavior. This paper seeks to present a survey of 18 techniques and a rigorous empirical study of their behavior across an extensive set of benchmarks. Our empirical study draws up a surprising observation: exact techniques are as efficient as the approximate ones, and therefore, we conclude with an optimistic view of opportunities for the design of approximate techniques with enhanced scalability. Motivated by the observation of an order of magnitude difference between the Virtual Best Solver and the best performing tool, we envision an exciting line of research focused on the development of portfolio solvers.