A Homological Approach to Belief Propagation and Bethe Approximations
Mathematical Physics
2020-07-28 v1 math.MP
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.
Keywords
Cite
@article{arxiv.1903.06088,
title = {A Homological Approach to Belief Propagation and Bethe Approximations},
author = {Olivier Peltre},
journal= {arXiv preprint arXiv:1903.06088},
year = {2020}
}
Comments
14 pages, submitted for the 2019 Geometric Science of Information colloquium