Asymmetric Topologies on Statistical Manifolds

Abstract

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.

arXiv comment8 pages, in Proceedings of the Second International Conference, GSI 2015, Palaiseau, France, October 28-30, 2015