Inference Schemes for M Best Solutions for Soft CSPs

The paper present a formalization of the m-best task within the unifying framework of semirings. As a consequence, known inference algorithms are defined and their correctness and completeness for the m-best task are immediately implied. We also describe and analyze a Bucket Elimination algorithm for solving the m-best task, elim-m-opt, presented in an earlier workshop and introduce an extension to the mini-bucket framework, yielding a collection of bounds for each of the m-best solutions. Some empirical demonstration of the algorithms and their potential for approximations are provided.

[1]  E. Lawler.  A PROCEDURE FOR COMPUTING THE K BEST SOLUTIONS TO DISCRETE OPTIMIZATION PROBLEMS AND ITS APPLICATION TO THE SHORTEST PATH PROBLEM , 1972 .

[2]  Prakash P. Shenoy,et al.  Probability propagation , 1990, Annals of Mathematics and Artificial Intelligence.

[3]  Jean-Louis Golmard,et al.  An algorithm directly finding the K most probable configurations in Bayesian networks , 1994, Int. J. Approx. Reason..

[4]  Thomas Schiex,et al.  Semiring-Based CSPs and Valued CSPs: Basic Properties and Comparison , 1995, Over-Constrained Systems.

[5]  D. Nilsson,et al.  An efficient algorithm for finding the M most probable configurationsin probabilistic expert systems , 1998, Stat. Comput..

[6]  Rina Dechter,et al.  Bucket Elimination: A Unifying Framework for Reasoning , 1999, Artif. Intell..

[7]  Robert J. McEliece,et al.  The generalized distributive law , 2000, IEEE Trans. Inf. Theory.

[8]  Adnan Darwiche,et al.  Decomposable negation normal form , 2001, JACM.

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

[10]  Y. Weiss,et al.  Finding the M Most Probable Configurations using Loopy Belief Propagation , 2003, NIPS 2003.

[11]  Paul Harrison Elliott.  Extracting the K best solutions from a valued and-or acyclic graph , 2007 .

[12]  Nic Wilson,et al.  Semiring induced valuation algebras: Exact and approximate local computation algorithms , 2008, Artif. Intell..

[13]  Amir Globerson,et al.  An LP View of the M-best MAP problem , 2009, NIPS.

[14]  R. Dechter,et al.  M best solutions over Graphical Models , 2010 .

[15]  Rina Dechter,et al.  Bucket and Mini-bucket Schemes for M Best Solutions over Graphical Models , 2011, GKR.