Tree and local computations in a cross-entropy minimization problem with marginal constraints

Title:

Tree and local computations in a cross-entropy minimization problem with marginal constraints

Creator:

Malvestuto, Francesco M.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:7043dc72-2e97-433a-b902-360155a7bc87
uuid:7043dc72-2e97-433a-b902-360155a7bc87

Subject:

cross-entropy, acrylic hypergraph, connection tree, junction tree, probabilistic database, and relation database

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In probability theory, Bayesian statistics, artificial intelligence and database theory the minimum cross-entropy principle is often used to estimate a distribution with a given set P of marginal distributions under the proportionality assumption with respect to a given "prior'' distribution q. Such an estimation problem admits a solution if and only if there exists an extension of P that is dominated by q. In this paper we consider the case that q is not given explicitly, but is specified as the maximum-entropy extension of an auxiliary set Q of distributions. There are three problems that naturally arise: (1) the existence of an extension of a distribution set (such as P and Q), (2) the existence of an extension of P that is dominated by the maximum entropy extension of Q, (3) the numeric computation of the minimum cross-entropy extension of P with respect to the maximum entropy extension of Q. In the spirit of a divide-and-conquer approach, we prove that, for each of the three above-mentioned problems, the global solution can be easily obtained by combining the solutions to subproblems defined at node level of a suitable tree.

Language:

English

Rights:

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

Coverage:

[621]-654

Source:

Kybernetika | 2010 Volume:46 | Number:4

Harvested from:

CDK

Metadata only:

false