FRANC, Alain; MICHEL, Goulard; PEYRARD, Nathalie

doi:10.1137/080736466

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

FRANC, Alain
Biodiversité, Gènes & Communautés [BioGeCo]

MICHEL, Goulard
Dynamiques Forestières dans l'Espace Rural [DYNAFOR]

PEYRARD, Nathalie
Unité de Biométrie et Intelligence Artificielle (ancêtre de MIAT) [UBIA]

Langue

Article de revue

Ce document a été publié dans

SIAM Journal on Discrete Mathematics. 2010, vol. 24, n° 3, p. 1104-1116

Society for Industrial and Applied Mathematics

Résumé en anglais

We consider the problem of specifying the joint distribution of a collection of variables with maximum entropy when a set of marginals are fixed. One can easily derive that the structure of the solution joint distribution is that of a graphical model. The potential functions are then marginals at some power. We address the following question, Under which conditions on the set of constraints is it possible to fully identify the canonical exponents in the maximum entropy solution as functions of the problem structure? Literature related to this topic is somewhat scattered in disciplines such as statistical mechanics, information theory, graph theory, and inference in graphical models. In this article we gather and link results from these different fields. From this, we show that for a particular class of constraints set on marginals, the chordal maximal coherent sets of constraints, it is possible to derive the canonical exponents of the graphical model solution of the maximum entropy problem as the numbers of occurrences of separators in an associated join tree. Conversely, we present sufficient conditions to ensure that a graphical model is a solution of a maximum entropy problem.< Réduire

Mots clés

ENTROPIE MAXIMALE

EXPOSANT CANONIQUE

Mots clés en anglais

MAXIMUM ENTROPY

GRAPHICAL MODELS

CHORDAL GRAPHS

GRAPHE CORDAL

GRAPHE TRIANGULE