Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Belief Optimization for Binary Networks: A Stable Alternative to Loopy Belief Propagation
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Expectation Propagation for approximate Bayesian inference
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
A new class of upper bounds on the log partition function
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Cluster Selection Based on Coupling for Gaussian Mean Fields
ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks
An edge deletion semantics for belief propagation and its practical impact on approximation quality
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Focusing generalizations of belief propagation on targeted queries
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 2
Convexifying the Bethe free energy
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
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Generalized belief propagation (GBP) has proven to be a promising technique for approximate inference tasks in AI and machine learning. However, the choice of a good set of clusters to be used in GBP has remained more of an art then a science until this day. This paper proposes a sequential approach to adding new clusters of nodes and their interactions (i.e. "regions") to the approximation. We first review and analyze the recently introduced region graphs and find that three kinds of operations ("split", "merge" and "death") leave the free energy and (under some conditions) the fixed points of GBP invariant. This leads to the notion of "weakly irreducible" regions as the natural candidates to be added to the approximation. Computational complexity of the GBP algorithm is controlled by restricting attention to regions with small "region-width". Combining the above with an efficient (i.e. local in the graph) measure to predict the improved accuracy of GBP leads to the sequential "region pursuit" algorithm for adding new regions bottom-up to the region graph. Experiments show that this algorithm can indeed perform close to optimally.