An Exact Algorithm for Solving Most Relevant Explanation in Bayesian Networks

Most Relevant Explanation (MRE) is a new inference task in Bayesian networks that finds the most relevant partial instantiation of target variables as an explanation for given evidence by maximizing the Generalized Bayes Factor (GBF). No exact algorithm has been developed for solving MRE previously. This paper fills the void and introduces a breadth-first branch-and-bound MRE algorithm based on a novel upper bound on GBF. The bound is calculated by decomposing the computation of the score to a set of Markov blankets of subsets of evidence variables. Our empirical evaluations show that the proposed algorithm scales up exact MRE inference significantly.

[1]  André Elisseeff,et al.  Explanation Trees for Causal Bayesian Networks , 2008, UAI.

[2]  Gregory F. Cooper,et al.  The ALARM Monitoring System: A Case Study with two Probabilistic Inference Techniques for Belief Networks , 1989, AIME.

[3]  I.,et al.  Weight of Evidence : A Brief Survey , 2006 .

[4]  Rina Dechter,et al.  AND/OR Branch-and-Bound search for combinatorial optimization in graphical models , 2009, Artif. Intell..

[5]  Changhe Yuan,et al.  Most Relevant Explanation: Properties, Algorithms, and Evaluations , 2009, UAI.

[6]  Adnan Darwiche,et al.  Node Splitting: A Scheme for Generating Upper Bounds in Bayesian Networks , 2007, UAI.

[7]  Adnan Darwiche,et al.  Solving MAP Exactly by Searching on Compiled Arithmetic Circuits , 2006, AAAI.

[8]  Adnan Darwiche,et al.  Approximating MAP using Local Search , 2001, UAI.

[9]  Branden Fitelson,et al.  Likelihoodism, Bayesianism, and relational confirmation , 2007, Synthese.

[10]  Robert Krauthgamer,et al.  A polylogarithmic approximation of the minimum bisection , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[11]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[12]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[13]  Fred Glover,et al.  Tabu Search: A Tutorial , 1990 .

[14]  Xi Chen,et al.  Evaluating computational models of explanation using human judgments , 2013, UAI.

[15]  Changhe Yuan,et al.  A General Framework for Generating Multivariate Explanations in Bayesian Networks , 2008, AAAI.

[16]  Adnan Darwiche,et al.  Solving MAP Exactly using Systematic Search , 2002, UAI.

[17]  Carmen Lacave,et al.  A review of explanation methods for Bayesian networks , 2002, The Knowledge Engineering Review.

[18]  Changhe Yuan,et al.  Most Relevant Explanation in Bayesian Networks , 2011, J. Artif. Intell. Res..

[19]  Changhe Yuan,et al.  Most Relevant Explanation: computational complexity and approximation methods , 2011, Annals of Mathematics and Artificial Intelligence.

[20]  Stuart J. Russell,et al.  Adaptive Probabilistic Networks with Hidden Variables , 1997, Machine Learning.

[21]  Changhe Yuan,et al.  Efficient Computation of Jointree Bounds for Systematic MAP Search , 2009, IJCAI.

[22]  Rina Dechter,et al.  Mini-buckets: A general scheme for bounded inference , 2003, JACM.

[23]  Steffen L. Lauritzen,et al.  Independence properties of directed markov fields , 1990, Networks.