Local and global properties in networks of processors (Extended Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Tree consistency and bounds on the performance of the max-product algorithm and its generalizations
Statistics and Computing
Walk-Sums and Belief Propagation in Gaussian Graphical Models
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
Message-passing algorithms for quadratic minimization
The Journal of Machine Learning Research
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We formulate a new approach to understanding the behavior of the min-sum algorithm by exploiting the properties of graph covers. First, we present a new, natural characterization of scaled diagonally dominant matrices in terms of graph covers; this result motivates our approach because scaled diagonal dominance is a known sufficient condition for the convergence of min-sum in the case of quadratic minimization. We use our understanding of graph covers to characterize the periodic behavior of the min-sum algorithm on a single cycle. Lastly, we explain how to extend the single cycle results to understand the 2-periodic behavior of min-sum for general pairwise MRFs. Some of our techniques apply more broadly, and we believe that by capturing the notion of indistinguishability, graph covers represent a valuable tool for understanding the abilities and limitations of general message-passing algorithms.