Classification into Kullback-Leibler balls in exponential families

JOURNAL OF MULTIVARIATE ANALYSIS

卷:150

Article

Katzur, Alexander¹  Kamps, Udo¹ 

[1] Rhein Westfal TH Aachen, Inst Stat, D-52056 Aachen, Germany

关键词: Bregman balls;    Bregman divergence;    Classification;    Convex duality;    Exponential families;    Functions of Legendre type (generalized) Chernoff information;    Itakura-Saito balls;    Itakura-Saito divergence;    Kullback-Leibler divergence (lower dimensional) Kullback-Leibler balls;    Minimal enclosing balls;    Multivariate normal distribution;    Sequential order statistics;   

DOI  :  10.1016/j.jmva.2016.05.007

来源: Elsevier

【 摘 要 】

A classification procedure for a two-class problem is introduced and analyzed, where the classes of probability density functions within a regular exponential family are represented by left-sided Kullback-Leibler balls of natural parameter vectors. If the class membership is known for a finite number of densities, only, classes are defined by constructing minimal enclosing left-sided Kullback-Leibler balls, which are seen to uniquely exist. A connection to Chernoff information between distributions is pointed out. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free