Approximation Algorithms for the Loop Cutset Problem

TL;DR

This paper introduces MGA, an approximation algorithm for the loop cutset problem in Bayesian networks, providing guarantees on solution size and demonstrating efficiency through testing on random graphs.

Contribution

The paper presents MGA, an approximation algorithm with a worst-case bound for finding small loop cutsets in Bayesian networks, improving over previous methods.

Findings

MGA guarantees a loop cutset size less than twice the minimum.

Average ratio of MGA's solution size to optimal is 1.22.

MGA performs well on randomly generated graphs.

Abstract

We show how to find a small loop curser in a Bayesian network. Finding such a loop cutset is the first step in the method of conditioning for inference. Our algorithm for finding a loop cutset, called MGA, finds a loop cutset which is guaranteed in the worst case to contain less than twice the number of variables contained in a minimum loop cutset. We test MGA on randomly generated graphs and find that the average ratio between the number of instances associated with the algorithms' output and the number of instances associated with a minimum solution is 1.22.