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arXiv · 1106.0225

Randomized Algorithms for the Loop Cutset Problem

R. Bar-Yehuda·A. Becker·D. Geiger
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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.

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R. Bar-Yehuda, A. Becker, D. Geiger. 2011-06-01. Randomized Algorithms for the Loop Cutset Problem. https://doi.org/10.1613/jair.638

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