Optimality conditions for maximizers of the information divergence from an exponential family

Title:

Optimality conditions for maximizers of the information divergence from an exponential family

Creator:

Matúš, František

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:d10d8265-750c-4815-b93f-4662e57fd5ad
uuid:d10d8265-750c-4815-b93f-4662e57fd5ad

Subject:

Kullback-Leibler divergence, relative entropy, exponential family, information projection, log-Laplace transform, cumulant generating function, directional derivatives, first order optimality conditions, convex funtions, and polytopes

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The information divergence of a probability measure P from an exponential family E over a finite set is defined as infimum of the divergences of P from Q subject to Q∈E. All directional derivatives of the divergence from E are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The first order conditions for P to be a maximizer of the divergence from E are presented, including new ones when P is not projectable to E .

Language:

English

Rights:

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

Coverage:

[731]-746

Source:

Kybernetika | 2007 Volume:43 | Number:5

Harvested from:

CDK

Metadata only:

false