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Bivariate distributions as saddle points of mutual information

Published online by Cambridge University Press:  14 July 2016

Geung Ho Kim  and
H. T. David
Geung Ho Kim
Affiliation:
Iowa State University
H. T. David
Affiliation:
Iowa State University
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Abstract

Fix a bivariate distribution F on X × Y, considered as a pair (α, {Fx}), where α is a marginal distribution on X and {Fx} is a collection of conditional distributions on Y. For essentially every (β,{Gx}) satisfying a certain pair of moment conditions determined by (α, {Fx}), J(β, {Fx}) ≦ J(α, {Fx}) ≦ J(α, {Gx}), where J is mutual information. This relates to two sorts of extremizations of mutual information of relevance to communication theory and statistics.

Keywords

CARTESIAN PRODUCTSCHANNEL CAPACITYMUTUAL INFORMATIONRATE DISTORTION FUNCTIONSADDLE POINTSSHANNON BOUNDS
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 523 - 530
Copyright
Copyright © Applied Probability Trust 1978 

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