4 papers
Minima and Critical Points of the Bethe Free Energy Are Invariant Under Deformation Retractions of Factor Graphs
Grégoire Sergeant-Perthuis, Léo Boitel
In graphical models, factor graphs, and more generally energy-based models, the interactions between variables are encoded by a graph, a hypergraph, or, in the most general case, a…
On the Functoriality of Belief Propagation Algorithms on finite Partially Ordered Sets
Grégoire Sergeant-Perthuis, Toby St Clere Smithe, Léo Boitel
Undirected graphical models are a widely used class of probabilistic models in machine learning that capture prior knowledge or putative pairwise interactions between variables. Th…
Interaction decomposition for Hilbert spaces
Grégoire Sergeant-Perthuis
The decomposition into interaction subspaces is an important result for graphical models and plays a central role for results on the linearized marginal problem; similarly the Chao…
Extra-fine sheaves and interaction decompositions
Daniel Bennequin, Olivier Peltre, Grégoire Sergeant-Perthuis +1
We introduce an original notion of extra-fine sheaf on a topological space, and a variant (hyper-extra-fine) for which Čech cohomology in strictly positive degree vanishes. We prov…