A Note on Divergences

Author:

Liang Xiao1

Affiliation:

1. Institute of Technology, University of Washington Tacoma, Tacoma, WA 98402, U.S.A.

Abstract

In many areas of neural computation, like learning, optimization, estimation, and inference, suitable divergences play a key role. In this note, we study the conjecture presented by Amari ( 2009 ) and find a counterexample to show that the conjecture does not hold generally. Moreover, we investigate two classes of [Formula: see text]-divergence (Zhang, 2004 ), weighted f-divergence and weighted [Formula: see text]-divergence, and prove that if a divergence is a weighted f-divergence, as well as a Bregman divergence, then it is a weighted [Formula: see text]-divergence. This result reduces in form to the main theorem established by Amari ( 2009 ) when [Formula: see text] [Formula: see text].

Publisher

MIT Press - Journals

Subject

Cognitive Neuroscience,Arts and Humanities (miscellaneous)

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