Computational complexity and approximization methods of most relevant explanation

Most Relevant Explanation (MRE) is a new approach to generating explanations for given evidence in Bayesian networks. MRE has a solution space containing all the partial instantiations of target variables and is extremely hard to solve. We show in this paper that the deci- sion problem of MRE is NP PP -complete. For large Bayesian networks, approximate methods may be the only feasible solutions. We observe that the solution space of MRE has a special lattice structure that con- nects all the potential solutions together. The connectiv- ity motivates us to develop several efficient local search methods for solving MRE. Empirical results show that these methods can efficiently find the optimal MRE so- lutions for majority of the test cases in our experiments. In this paper, we develop several local search methods for solving MRE. Local methods have been shown to be effec- tive in solving MAP problems in Bayesian networks (Park & Darwiche 2001). We further observe that the solution space of MRE has a special lattice structure that connects all the potential solutions, which motivates us to design several lo- cal search strategies to find high-quality solutions efficiently. Empirical results show that these local search methods are not only efficient but also able to find the optimal solutions for most of the test cases in our experiments. The remainder of the paper is structured as follows. Sec- tion 2 reviews the formulation of Most Relevant Expla- nation. Section 3 proves that the decision problem of MRE is NP PP -complete. Section 4 develops several local search methods for solving MRE, including forward search, forward-backward search, and partial exhaustive search. Fi- nally, Section 5 presents the empirical evaluations of these local MRE methods on a set of benchmark Bayesian net- works.