Loop Corrections for Approximate Inference on Factor Graphs
The Journal of Machine Learning Research
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Loop Calculus for satisfiability
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
Approximate inference on planar graphs using loop calculus and belief propagation
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Approximate Inference on Planar Graphs using Loop Calculus and Belief Propagation
The Journal of Machine Learning Research
Join-graph propagation algorithms
Journal of Artificial Intelligence Research
New graph polynomials from the bethe approximation of the ising partition function
Combinatorics, Probability and Computing
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Recently, Chertkov and Chernyak (2006b) derived an exact expression for the partition sum (normalization constant) corresponding to a graphical model, which is an expansion around the belief propagation (BP) solution. By adding correction terms to the BP free energy, one for each "generalized loop" in the factor graph, the exact partition sum is obtained. However, the usually enormous number of generalized loops generally prohibits summation over all correction terms. In this article we introduce truncated loop series BP (TLSBP), a particular way of truncating the loop series of Chertkov & Chernyak by considering generalized loops as compositions of simple loops. We analyze the performance of TLSBP in different scenarios, including the Ising model on square grids and regular random graphs, and on PROMEDAS, a large probabilistic medical diagnostic system. We show that TLSBP often improves upon the accuracy of the BP solution, at the expense of increased computation time. We also show that the performance of TLSBP strongly depends on the degree of interaction between the variables. For weak interactions, truncating the series leads to significant improvements, whereas for strong interactions it can be ineffective, even if a high number of terms is considered.