Approximating the Partition Function by Deleting and then Correcting for Model Edges

TL;DR

This paper introduces a novel method for approximating the partition function by simplifying the model through edge deletion and then correcting for these deletions, balancing accuracy and computational complexity.

Contribution

It presents a new framework that combines edge deletion with correction, generalizing existing approximations like Bethe free energy, and demonstrates its theoretical and practical benefits.

Findings

The approach effectively balances approximation quality and computational complexity.

Empirical results show improved accuracy over traditional methods.

The framework generalizes the Bethe free energy approximation.

Abstract

We propose an approach for approximating the partition function which is based on two steps: (1) computing the partition function of a simplified model which is obtained by deleting model edges, and (2) rectifying the result by applying an edge-by-edge correction. The approach leads to an intuitive framework in which one can trade-off the quality of an approximation with the complexity of computing it. It also includes the Bethe free energy approximation as a degenerate case. We develop the approach theoretically in this paper and provide a number of empirical results that reveal its practical utility.