A Homological Approach to Belief Propagation and Bethe Approximations
arXiv:1903.06088 · doi:10.1007/978-3-030-26980-7_23
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.
14 pages, submitted for the 2019 Geometric Science of Information colloquium