Randomized Algorithms for the Loop

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 6 k kn) steps with probability at least 1 ? (1 ? 1 6 k) c6 k , where c > 1 is a constant speciied 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 nds a loop cutset that is closer to the minimum weight loop cutset than the ones found by the best deterministic algorithms known.