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Bivariate distributions as saddle points of mutual information
Published online by Cambridge University Press: 14 July 2016
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.
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- Copyright © Applied Probability Trust 1978