Asymmetric Topologies on Statistical Manifolds

Asymmetric information distances are used to define asymmetric norms and quasimetrics on the statistical manifold and its dual space of random variables. Quasimetric topology, generated by the Kullback-Leibler (KL) divergence, is considered as the main example, and some of its topological properties...

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Bibliographic Details
Main Author:	Belavkin, Roman V
Format:	Journal Article
Language:	English
Published:	29-07-2015
Subjects:	Computer Science - Information Theory Mathematics - Functional Analysis Mathematics - General Topology Mathematics - Information Theory
Online Access:	Get full text
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Summary:	Asymmetric information distances are used to define asymmetric norms and quasimetrics on the statistical manifold and its dual space of random variables. Quasimetric topology, generated by the Kullback-Leibler (KL) divergence, is considered as the main example, and some of its topological properties are investigated.
DOI:	10.48550/arxiv.1507.08229