Stochastic Local Search for Solving the Most Probable Explanation Problem in Bayesian Networks

In this thesis, we develop and study novel Stochastic Local Search (SLS) algorithms for solving the Most Probable Explanation (MPE) problem in graphical models, that is, to find the most probable instantiation of all variables V in the model, given the observed values E = e of a subset E of V. SLS algorithms have been applied to the MPE problem before [KD99b, Par02], but none of the previous SLS algorithms pays sufficient attention to such important concerns as algorithmic complexity per search step, search stagnation, and thorough parameter tuning. We remove these shortcomings of previous SLS algorithms for MPE, improving their efficiency by up to six orders of magnitude. In a thorough experimental analysis, we demonstrate how each of the novel components of our algorithms substantially contributes to their high performance. A comparison with an anytime version of the prominent Mini-Buckets algorithm [DR03] and the exact algorithm Branchand-Bound with static Mini-Buckets heuristic (BBMB) [KD99a, MKD03] shows that our best algorithm outperforms these approaches on most MPE instances we study. We also show that our SLS algorithms scale much better in terms of a number of important instance characteristics, namely the number of variables, domain size, node degree, and induced width of the underlying graphical model.