Convergent message passing algorithms - A unifying view

Talya Meltzer*, Amir Globerson, Yair Weiss

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

88 Scopus citations


Message-passing algorithms have emerged as powerful techniques for approximate inference in graphical models. When these algorithms converge, they can be shown to find local (or sometimes even global) optima of variational formulations to the inference problem. But many of the most popular algorithms are not guaranteed to converge. This has lead to recent interest in convergent message-passing algorithms. In this paper, we present a unified view of convergent message-passing algorithms. We present a simple derivation of an abstract algorithm, tree-consistency bound optimization (TCBO) that is provably convergent in both its sum and max product forms. We then show that many of the existing convergent algorithms are instances of our TCBO algorithm, and obtain novel convergent algorithms "for free" by exchanging maximizations and summations in existing algorithms. In particular, we show that Wainwright's non-convergent sum-product algorithm for tree based variational bounds, is actually convergent with the right update order for the case where trees are monotonic chains.

Original languageAmerican English
Title of host publicationProceedings of the 25th Conference on Uncertainty in Artificial Intelligence, UAI 2009
PublisherAUAI Press
Number of pages9
StatePublished - 2009

Publication series

NameProceedings of the 25th Conference on Uncertainty in Artificial Intelligence, UAI 2009


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