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arXiv · 1903.06088

A Homological Approach to Belief Propagation and Bethe Approximations

Olivier Peltre
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Abstract

We introduce a differential complex of local observables given a decomposition of a global set of random variables into subsets. Its boundary operator allows us to define a transport equation equivalent to Belief Propagation. This definition reveals a set of conserved quantities under Belief Propagation and gives new insight on the relationship of its equilibria with the critical points of Bethe free energy.

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Olivier Peltre. 2019-03-14. A Homological Approach to Belief Propagation and Bethe Approximations. https://doi.org/10.1007/978-3-030-26980-7_23

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