Approximation Algorithms for the Loop Cutset Problem
This work addresses a key bottleneck in probabilistic inference for Bayesian networks, offering an incremental improvement with practical performance gains.
The paper tackles the problem of finding a small loop cutset in Bayesian networks, which is crucial for inference via conditioning, and presents the MGA algorithm that guarantees a worst-case approximation ratio of less than 2 and achieves an average ratio of 1.22 on randomly generated graphs.
We show how to find a small loop curser in a Bayesian network. Finding such a loop cutset is the first step in the method of conditioning for inference. Our algorithm for finding a loop cutset, called MGA, finds a loop cutset which is guaranteed in the worst case to contain less than twice the number of variables contained in a minimum loop cutset. We test MGA on randomly generated graphs and find that the average ratio between the number of instances associated with the algorithms' output and the number of instances associated with a minimum solution is 1.22.