Initialization and Restart in Stochastic Local Search: Computing a Most Probable Explanation in Bayesian Networks

Abstract

Abstract-For hard computational problems, stochastic local search has proven to be a competitive approach to finding optimal or approximately optimal problem solutions. Two key research questions for stochastic local search algorithms are: Which algorithms are effective for initialization? When should the search process be restarted? In the present work, we investigate these research questions in the context of approximate computation of most probable explanations (MPEs) in Bayesian networks (BNs). We introduce a novel approach, based on the Viterbi algorithm, to explanation initialization in BNs. While the Viterbi algorithm works on sequences and trees, our approach works on BNs with arbitrary topologies. We also give a novel formalization of stochastic local search, with focus on initialization and restart, using probability theory and mixture models. Experimentally, we apply our methods to the problem of MPE computation, using a stochastic local search algorithm known as Stochastic Greedy Search. By carefully optimizing both initialization and restart, we reduce the MPE search time for application BNs by several orders of magnitude compared to using uniform at random initialization without restart. On several BNs from applications, the performance of Stochastic Greedy Search is competitive with clique tree clustering, a state-of-the-art exact algorithm used for MPE computation in BNs.

Portfolios in Stochastic Local Search: Efficiently Computing Most Probable Explanations in Bayesian Networks

“…Section 8 concludes and discusses future work. This article extends and revises our earlier reports on SGS [54,60].…”

“…Stochastic local search (SLS) algorithms have proven to be competitive in solving computationally hard problems including satisfiability (SAT) [27,35,75,77,78], the most probable explanation [39,41,48,54,60], and the maximum a posteriori (MAP) hypothesis [67,68]. Unfortunately, the theoretical understanding of SLS algorithms has been lagging [33], and despite recent progress [32,57,62] it is clear that further advances are needed. This work is part of a larger research effort where the ultimate goal is the development of highly adaptive but well-understood SLS algorithms, including SLS algorithms for MPE computation in BNs.…”

“…Portfolio methods support the combination of a wide range of different algorithms, and have been identified as a promising research direction [25,26,38,39,60,84]. This article provides an improved understanding of the role of portfolios of heuristics in stochastic local search.…”

“…Our approach is implemented in the Stochastic Greedy Search (SGS) system; two SGS algorithms called SimpleSGS and OperatorSGS are presented in this article. The OperatorSGS algorithm is a portfolio-based [25,38,60,84] approach to MPE computation using SLS. It provides a flexible and general framework for stochastic explanation initialization and search.…”

“…In this article we highlight two reasons for SGS's success in application BNs, namely the ability to exploit different search operators in OperatorSGS as well as the use of the additive measure of gain. (Another significant component in the success of SGS is the stochastic initialization portfolio, including its dynamic programming and forward simulation algorithms [60,62]. The heuristics in the initialization portfolio suggest good starting points to the stochastic local search component of SGS; see also [41,67,68].…”