96 citations · 109 across the 12 of their papers we have counts for
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math-ph2023★ 1 cited
Local Max-Entropy and Free Energy Principles, Belief Diffusions and their Singularities
Olivier Peltre
A comprehensive picture of three Bethe-Kikuchi variational principles including their relationship to belief propagation (BP) algorithms on hypergraphs is given. The structure of B…
math-ph2020★ 1 cited
Message-Passing Algorithms and Homology
Olivier Peltre
This PhD thesis lays out algebraic and topological structures relevant for the study of probabilistic graphical models. Marginal estimation algorithms are introduced as diffusion e…
math-ph2019★ 4 cited
A Homological Approach to Belief Propagation and Bethe Approximations
Olivier Peltre
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 transpo…