Approximation 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(c6kkn) steps with probability at least 1 ; (1 ; 1 6k )c6k , 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.

• Type: Conference
• Year: 1994
• Where: UAI
• Authors: Ann Becker, Dan Geiger
• Keywords: Loop Cutset, Minimum Weight Loop, UAI 1994, UAI 2008, Weight Loop Cutset