Randomized Algorithms for the Loop Cutset Problem

TL;DR

This paper introduces a randomized algorithm that efficiently finds near-optimal minimum weight loop cutsets in Bayesian networks, improving inference methods with probabilistic guarantees and empirical performance.

Contribution

It presents a novel randomized algorithm for finding minimum weight loop cutsets with probabilistic guarantees and demonstrates empirical improvements over existing deterministic methods.

Findings

Algorithm finds minimum loop cutset with high probability within specified steps.

Empirical results show the algorithm often outperforms deterministic algorithms.

Probabilistic bounds provide theoretical guarantees for the algorithm's success.

Abstract

We show how to find a minimum weight loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in the method of conditioning for inference. Our randomized algorithm for finding a loop cutset outputs a minimum loop cutset after O(c 6^k kn) steps with probability at least 1 - (1 - 1/(6^k))^c6^k, where c > 1 is a constant specified by the user, k is the minimal size of a minimum weight loop cutset, and n is the number of vertices. We also show empirically that a variant of this algorithm often finds a loop cutset that is closer to the minimum weight loop cutset than the ones found by the best deterministic algorithms known.