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• W2946469510 abstract "Belief propagation is a fundamental message-passing algorithm for probabilistic reasoning and inference in graphical models. While it is known to be exact on trees, in most applications belief propagation is run on graphs with cycles. Understanding the behavior of loopy belief propagation has been a major challenge for researchers in machine learning, and positive convergence results for BP are known under strong assumptions which imply the underlying graphical model exhibits decay of correlations. We show that under a natural initialization, BP converges quickly to the global optimum of the Bethe free energy for Ising models on arbitrary graphs, as long as the Ising model is emph{ferromagnetic} (i.e. neighbors prefer to be aligned). This holds even though such models can exhibit long range correlations and may have multiple suboptimal BP fixed points. We also show an analogous result for iterating the (naive) mean-field equations; perhaps surprisingly, both results are dimension-free in the sense that a constant number of iterations already provides a good estimate to the Bethe/mean-field free energy." @default.
• W2946469510 created "2019-05-29" @default.
• W2946469510 creator A5003106042 @default.
• W2946469510 date "2019-05-24" @default.
• W2946469510 modified "2023-09-23" @default.
• W2946469510 title "Fast Convergence of Belief Propagation to Global Optima: Beyond Correlation Decay" @default.
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