Pushing Forward Marginal MAP with Best-First Search

Marginal MAP is known to be a difficult task for graphical models, particularly because the evaluation of each MAP assignment involves a conditional likelihood computation. In order to minimize the number of likelihood evaluations, we focus in this paper on best-first search strategies for exploring the space of partial MAP assignments. We analyze the potential relative benefits of several best-first search algorithms and demonstrate their effectiveness against recent branch and bound schemes through extensive empirical evaluations. Our results show that best-first search improves significantly over existing depth-first approaches, in many cases by several orders of magnitude, especially when guided by relatively weak heuristics.

[1]  Rina Dechter,et al.  Mini-buckets: a general scheme for approximating inference , 2002 .

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

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

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

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

[6]  Akihiro Kishimoto,et al.  Recursive Best-First AND/OR Search for Optimization in Graphical Models , 2014, UAI.

[7]  Nils J. Nilsson,et al.  Principles of Artificial Intelligence , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Rina Dechter,et al.  AND/OR Search for Marginal MAP , 2014, UAI.

[9]  Qiang Liu,et al.  Bounding the Partition Function using Holder's Inequality , 2011, ICML.

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

[11]  Richard E. Korf,et al.  Linear-Space Best-First Search , 1993, Artif. Intell..

[12]  Rina Dechter,et al.  Memory intensive AND/OR search for combinatorial optimization in graphical models , 2009, Artif. Intell..

[13]  Rina Dechter,et al.  AND/OR search spaces for graphical models , 2007, Artif. Intell..

[14]  James D. Park,et al.  MAP Complexity Results and Approximation Methods , 2002, UAI.

[15]  Dan Roth,et al.  On the Hardness of Approximate Reasoning , 1993, IJCAI.