Randomized Algorithms for the Loop Cutset Problem

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