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Generalization of graph network inferences in higher-order probabilistic graphical models
Probabilistic graphical models provide a powerful tool to describe complex
statistical structure, with many real-world applications in science and
engineering from controlling robotic arms to understanding neuronal
computations. A major challenge for these graphical models is that inferences
such as marginalization are intractable for general graphs. These inferences
are often approximated by a distributed message-passing algorithm such as
Belief Propagation, which does not always perform well on graphs with cycles,
nor can it always be easily specified for complex continuous probability
distributions. Such difficulties arise frequently in expressive graphical
models that include intractable higher-order interactions. In this paper we
construct iterative message-passing algorithms using Graph Neural Networks
defined on factor graphs to achieve fast approximate inference on graphical
models that involve many-variable interactions. Experimental results on several
families of graphical models demonstrate the out-of-distribution generalization
capability of our method to different sized graphs, and indicate the domain in
which our method gains advantage over Belief Propagation.Comment: 9 pages, 2 figure
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