Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Fast parallel algorithms for graph matching problems
Fast parallel algorithms for graph matching problems
A revolution: belief propagation in graphs with cycles
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Truncating the Loop Series Expansion for Belief Propagation
The Journal of Machine Learning Research
Loopy belief propagation for approximate inference: an empirical study
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Approximate inference and constrained optimization
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Codes on graphs: normal realizations
IEEE Transactions on Information Theory
Constructing free-energy approximations and generalized belief propagation algorithms
IEEE Transactions on Information Theory
A new class of upper bounds on the log partition function
IEEE Transactions on Information Theory
Decomposition and Approximation of Loopy Bayesian Networks
Fundamenta Informaticae
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We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. The loop calculus (Chertkov and Chernyak, 2006b) allows to express the exact partition function Z of a graphical model as a finite sum of terms that can be evaluated once the belief propagation (BP) solution is known. In general, full summation over all correction terms is intractable. We develop an algorithm for the approach presented in Chertkov et al. (2008) which represents an efficient truncation scheme on planar graphs and a new representation of the series in terms of Pfaffians of matrices. We analyze in detail both the loop series and the Pfaffian series for models with binary variables and pairwise interactions, and show that the first term of the Pfaffian series can provide very accurate approximations. The algorithm outperforms previous truncation schemes of the loop series and is competitive with other state-of-the-art methods for approximate inference.