Classification into Kullback–Leibler balls in exponential families

Alexander Katzur and Udo Kamps

Journal of Multivariate Analysis, 2016, vol. 150, issue C, 75-90

Abstract: 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.

Keywords: 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 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2016.05.007

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