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

Creator:
Matúš, František
Format:
bez média and svazek
Type:
model:article and TEXT
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
Language:
English
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 .
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public