Boosting Search with Variable Elimination
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
Memory intensive AND/OR search for combinatorial optimization in graphical models
Artificial Intelligence
Reasoning from last conflict(s) in constraint programming
Artificial Intelligence
Soft arc consistency revisited
Artificial Intelligence
Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning
Tree decomposition with applications to constraint processing
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
Causal independence for probability assessment and inference using Bayesian networks
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Propagating soft table constraints
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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We propose a new additive decomposition of probability tables that preserves equivalence of the joint distribution while reducing the size of potentials, without extra variables. We formulate the Most Probable Explanation (MPE) problem in belief networks as a Weighted Constraint Satisfaction Problem (WCSP). Our pairwise decomposition allows to replace a cost function with smaller-arity functions. The resulting pairwise decomposed WCSP is then easier to solve using state-of-the-art WCSP techniques. Although testing pairwise decomposition is equivalent to testing pairwise independence in the original belief network, we show how to efficiently test and enforce it, even in the presence of hard constraints. Furthermore, we infer additional information from the resulting nonbinary cost functions by projecting&subtracting them on binary functions. We observed huge improvements by preprocessing with pairwise decomposition and project&subtract compared to the current state-of-the-art solvers on two difficult sets of benchmark.