Comparison of two methods for approximation of probability distributions with prescribed marginals

Title:

Comparison of two methods for approximation of probability distributions with prescribed marginals

Creator:

Perez, Albert and Studený, Milan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:5a4fe66a-045e-4f01-a8c1-6d99f4504e87
uuid:5a4fe66a-045e-4f01-a8c1-6d99f4504e87

Subject:

marginal problem, relative entropy, dependence structure simplificaton, explicit expression approximation, multiinformation, decomposable model, and asteroid

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let P be a discrete multidimensional probability distribution over a finite set of variables N which is only partially specified by the requirement that it has prescribed given marginals {PA;A∈\SS}, where \SS is a class of subsets of N with ⋃\SS=N. The paper deals with the problem of approximating P on the basis of those given marginals. The divergence of an approximation P^ from P is measured by the relative entropy H(P|P^). Two methods for approximating P are compared. One of them uses formerly introduced concept of {\em dependence structure simplification\/} (see Perez \cite{Per79}). The other one is based on an {\em explicit expression}, which has to be normalized. We give examples showing that neither of these two methods is universally better than the other. If one of the considered approximations P^ really has the prescribed marginals then it appears to be the distribution P with minimal possible multiinformation. A simple condition on the class \SS implying the existence of an approximation P^ with prescribed marginals is recalled. If the condition holds then both methods for approximating P give the same result.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[591]-618

Source:

Kybernetika | 2007 Volume:43 | Number:5

Harvested from:

CDK

Metadata only:

false