Approximating the Permanent with Belief Propagation

TL;DR

This paper introduces an efficient belief propagation-based method to approximate matrix permanents by formulating a probability distribution whose partition function equals the permanent, achieving faster computation and demonstrating practical advantages.

Contribution

It presents a novel belief propagation approach to approximate the permanent with improved speed and accuracy, linking the permanent to a partition function in a probabilistic model.

Findings

Algorithm requires O(n^2) time per iteration.

Demonstrates practical advantages of the approximation.

Provides speedups over standard belief propagation methods.

Abstract

This work describes a method of approximating matrix permanents efficiently using belief propagation. We formulate a probability distribution whose partition function is exactly the permanent, then use Bethe free energy to approximate this partition function. After deriving some speedups to standard belief propagation, the resulting algorithm requires $(n^2)$ time per iteration. Finally, we demonstrate the advantages of using this approximation.