Bidirectional Heuristic Search to Find the Optimal Bayesian Network Structure

Abstract Bayesian networks have many applications. Learning the optimal structure of a Bayesian network has always been important in this respect. In this paper, a bidirectional heuristic search algorithm is proposed for the order graph space commonly used in a Bayesian network. At the same time, heuristic functions that are admissible and consistent in terms of both forward and backward search are proposed to ensure convergence of the algorithm to the optimal solution. The experimental results show that, compared with traditional unidirectional heuristic search, in most cases, the bidirectional heuristic search proposed in this paper needs to expand fewer states, the convergence efficiency is higher, and less running time is needed.

[1]  David Maxwell Chickering,et al.  Learning Bayesian Networks is NP-Complete , 2016, AISTATS.

[2]  Kewei Tu,et al.  Learning Bayesian network structures under incremental construction curricula , 2017, Neurocomputing.

[3]  Constantin F. Aliferis,et al.  The max-min hill-climbing Bayesian network structure learning algorithm , 2006, Machine Learning.

[4]  Changhe Yuan,et al.  Learning Optimal Bayesian Networks: A Shortest Path Perspective , 2013, J. Artif. Intell. Res..

[5]  David Maxwell Chickering,et al.  Large-Sample Learning of Bayesian Networks is NP-Hard , 2002, J. Mach. Learn. Res..

[6]  Mohammad Reza Meybodi,et al.  BNC-PSO: structure learning of Bayesian networks by Particle Swarm Optimization , 2016, Inf. Sci..

[7]  Eric A. Hansen,et al.  Breadth-first heuristic search , 2004, Artif. Intell..

[8]  Richard E. Korf,et al.  Disjoint pattern database heuristics , 2002, Artif. Intell..

[9]  Hui Liu,et al.  A new hybrid method for learning bayesian networks: Separation and reunion , 2017, Knowl. Based Syst..

[10]  Changhe Yuan,et al.  An Improved Admissible Heuristic for Learning Optimal Bayesian Networks , 2012, UAI.

[11]  Brandon M. Malone,et al.  Empirical hardness of finding optimal Bayesian network structures: algorithm selection and runtime prediction , 2017, Machine Learning.

[12]  David Heckerman,et al.  A Tutorial on Learning with Bayesian Networks , 1999, Innovations in Bayesian Networks.

[13]  Hermann Kaindl,et al.  Bidirectional Heuristic Search Reconsidered , 1997, J. Artif. Intell. Res..

[14]  Jose Miguel Puerta,et al.  Ant colony optimization for learning Bayesian networks , 2002, Int. J. Approx. Reason..

[15]  Changhe Yuan,et al.  Memory-Efficient Dynamic Programming for Learning Optimal Bayesian Networks , 2011, AAAI.

[16]  Rina Dechter,et al.  Generalized best-first search strategies and the optimality of A* , 1985, JACM.

[17]  James Cussens,et al.  Integer Linear Programming for the Bayesian network structure learning problem , 2017, Artif. Intell..

[18]  Peter van Beek,et al.  Machine Learning of Bayesian Networks Using Constraint Programming , 2015, CP.

[19]  Changhe Yuan,et al.  Evaluating Anytime Algorithms for Learning Optimal Bayesian Networks , 2013, UAI.

[20]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[21]  Mikko Koivisto,et al.  Exact Bayesian Structure Discovery in Bayesian Networks , 2004, J. Mach. Learn. Res..