Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast Convergence of Belief Propagation to Global Optima: Beyond
  Correlation Decay   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.

18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph