5 citations · 15 across the 12 of their papers we have counts for
12 papers
Exact Algebraic Computation of Learning Coefficients for Two-Dimensional Singular Models
Grégoire Sergeant-Perthuis, Elias Tsigaridas, Jules Tsukahara
Classical information criteria such as the Bayesian Information Criterion (BIC) rely on regularity assumptions that break down for singular models, leading to incorrect model selec…
Reduction of Probabilistic Chemical Reaction Networks
Mauricio Montes, Gregoire Sergeant-Perthuis
Programming adaptive behaviors at the cellular level is a long-standing goal that raises the question of how probabilistic computation can be implemented in biochemical systems. Ch…
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…
Compositional statistical mechanics, entropy and variational inference
Grégoire Sergeant-Perthuis
In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on…
On Non-Linear operators for Geometric Deep Learning
Grégoire Sergeant-Perthuis, Jakob Maier, Joan Bruna +1
This work studies operators mapping vector and scalar fields defined over a manifold , and which commute with its group of diffeomorphisms .…
Regionalized Optimization
Grégoire Sergeant-Perthuis
We propose a theoretical framework for non redundant reconstruction of a global loss from a collection of local ones under constraints given by a functor; we call this loss the reg…
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 (upper) extra-fine sheaf on a topological space, for which Čech cohomology in strictly positive degree vanishes. We apply this notion when the to…
Interaction decomposition for presheaves
Grégoire Sergeant-Perthuis
Consider a collection of vector subspaces of a given vector space and a collection of projectors on these vector spaces, can we decompose the vector space into a product of vector…
Intersection property and interaction decomposition
Grégoire Sergeant-Perthuis
The decomposition into interaction subspaces is a hierarchical decomposition of the spaces of cylindrical functions of a finite product space, also called factor spaces. It is an i…
Bayesian/Graphoid intersection property for factorisation spaces
Grégoire Sergeant-Perthuis
We remark that Pearl's Graphoid intersection property, also called intersection property in Bayesian networks, is a particular case of a general intersection property, in the sense…