Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Semiring-based constraint satisfaction and optimization
Journal of the ACM (JACM)
Local computation with valuations from a commutative semigroup
Annals of Mathematics and Artificial Intelligence
Mini-buckets: A general scheme for bounded inference
Journal of the ACM (JACM)
Using weighted MAX-SAT engines to solve MPE
Eighteenth national conference on Artificial intelligence
Constraint Processing
Arc consistency for soft constraints
Artificial Intelligence
Semiring induced valuation algebras: Exact and approximate local computation algorithms
Artificial Intelligence
Modeling and Reasoning with Bayesian Networks
Modeling and Reasoning with Bayesian Networks
Enhancing constraints manipulation in semiring-based formalisms
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Unifying tree decompositions for reasoning in graphical models
Artificial Intelligence
Join-graph propagation algorithms
Journal of Artificial Intelligence Research
A scheme for approximating probabilistic inference
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
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Graphical models are one of the most prominent frameworks to model complex systems and efficiently query them. Their underlying algebraic properties are captured by a valuation structure that, most usually, is a semiring. Depending on the semiring of choice, we can capture probabilistic models, constraint networks, cost networks, etc. In this paper we address the partitioning problem which occurs in many approximation techniques such as mini-bucket elimination and joingraph propagation algorithms. Roghly speaking, subject to complexity bounds, the algorithm needs to find a partition of a set of factors such that best approximates the whole set. While this problem has been addressed in the past in a particular case, we present here a general description. Furthermore, we also propose a general partitioning scheme. Our proposal is general in the sense that it is presented in terms of a generic semiring with the only additional requirements of a division operation and a refinement of its order. The proposed algorithm instantiates to the particular task of computing the probability of evidence, but also applies directly to other important reasoning tasks. We demonstrate its good empirical behaviour on the problem of computing the most probable explanation.