Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
Decomposable negation normal form
Journal of the ACM (JACM)
An efficient algorithm for finding the M most probable configurationsin probabilistic expert systems
Statistics and Computing
Mini-buckets: A general scheme for bounded inference
Journal of the ACM (JACM)
Semiring-Based CSPs and Valued CSPs: Basic Properties and Comparison
Over-Constrained Systems
AND/OR search spaces for graphical models
Artificial Intelligence
Semiring induced valuation algebras: Exact and approximate local computation algorithms
Artificial Intelligence
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
K*: A heuristic search algorithm for finding the k shortest paths
Artificial Intelligence
The generalized distributive law
IEEE Transactions on Information Theory
Algorithms for generating ordered solutions for explicit and/or structures
Journal of Artificial Intelligence Research
Diverse M-best solutions in markov random fields
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part V
Algorithms for generating ordered solutions for explicit AND/OR structures: extended abstract
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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The paper focuses on the task of generating the first m best solutions for a combinatorial optimization problem defined over a graphical model (e.g., the m most probable explanations for a Bayesian network). We show that the m-best task can be expressed within the unifying framework of semirings making known inference algorithms defined and their correctness and completeness for the m-best task immediately implied. We subsequently describe elim-m-opt, a new bucket elimination algorithm for solving the m-best task, provide algorithms for its defining combination and marginalization operators and analyze its worst-case performance. An extension of the algorithm to the mini-bucket framework provides bounds for each of the m best solutions. Empirical demonstrations of the algorithms with emphasis on their potential for approximations are provided.