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2016•Unpublished venueRequires access

A characterization of statistical manifolds on which the relative entropy is a Bregman divergence

Hiroshi Nagaoka

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Abstract

It is well known that the relative entropy (Kullback-Leibler divergence) is represented in the form of Bregman divergence on exponential families and mixture families for some coordinate systems. We give a characterization of the class of statistical manifolds (smooth manifolds of probability mass functions on finite sample spaces) having coordinate systems for which the relative entropy is a Bregman divergence.

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What this paper is about

It is well known that the relative entropy (Kullback-Leibler divergence) is represented in the form of Bregman divergence on exponential families and mixture families for some coordinate systems. We give a characterization of the class of statistical manifolds (smooth manifolds of probability mass functions on finite sample spaces) having coordinate systems for which the relative entropy is a Bregman divergence.

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Available abstract

It is well known that the relative entropy (Kullback-Leibler divergence) is represented in the form of Bregman divergence on exponential families and mixture families for some coordinate systems. We give a characterization of the class of statistical manifolds (smooth manifolds of probability mass functions on finite sample spaces) having coordinate systems for which the relative entropy is a Bregman divergence.

Key concepts: Bregman divergence, Kullback–Leibler divergence, Divergence (linguistics), Mathematics, Entropy (arrow of time), Exponential family, Quantum relative entropy, Applied mathematics

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