Chordal graphs to identify graphical model solutions of maximum of entropy under constraints on marginals
Language
en
Article de revue
This item was published in
SIAM Journal on Discrete Mathematics. 2010, vol. 24, n° 3, p. 1104-1116
Society for Industrial and Applied Mathematics
English Abstract
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 ...Read more >
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.Read less <
Keywords
ENTROPIE MAXIMALE
EXPOSANT CANONIQUE
English Keywords
MAXIMUM ENTROPY
GRAPHICAL MODELS
CHORDAL GRAPHS
GRAPHE CORDAL
GRAPHE TRIANGULE
Origin
Hal imported