On a Variational Definition for the Jensen-Shannon Symmetrization of Distances based on the Information Radius

02/19/2021
by   Frank Nielsen, et al.
0

We generalize the Jensen-Shannon divergence by considering a variational definition with respect to a generic mean extending thereby the notion of Sibson's information radius. The variational definition applies to any arbitrary distance and yields another way to define a Jensen-Shannon symmetrization of distances. When the variational optimization is further constrained to belong to prescribed probability measure families, we get relative Jensen-Shannon divergences and symmetrizations which generalize the concept of information projections. Finally, we discuss applications of these variational Jensen-Shannon divergences and diversity indices to clustering and quantization tasks of probability measures including statistical mixtures.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/08/2019

On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means

The Jensen-Shannon divergence is a renown bounded symmetrization of the ...
research
12/02/2019

On a generalization of the Jensen-Shannon divergence

The Jensen-Shannon divergence is a renown bounded symmetrization of the ...
research
09/21/2010

A family of statistical symmetric divergences based on Jensen's inequality

We introduce a novel parametric family of symmetric information-theoreti...
research
02/20/2023

Metrization of powers of the Jensen-Shannon divergence

Metrization of statistical divergences is useful in both theoretical and...
research
12/03/2021

Introduction to Logical Entropy and its Relationship to Shannon Entropy

We live in the information age. Claude Shannon, as the father of the inf...
research
08/01/2019

General Information Theory: Time and Information

This paper introduces time into information theory, gives a more accurat...
research
02/26/2021

Moreau-Yosida f-divergences

Variational representations of f-divergences are central to many machine...

Please sign up or login with your details

Forgot password? Click here to reset