A Dual Optimization Framework for Some Problems of Information Theory and Statistics.

摘要

A new dual optimization framework for some problems of information theory and statistics is developed in the form of dual convex programming problems and their duality theory. It extends the work for finite discrete distributions to the case of general measures. Although the primal problem (constrained relative entropy) is an infinite dimensional one, the dual problem is a finite dimensional one without constraints and involving only exponential and linear terms. Applications range from mathematical statistics and statistical mechanics to traffic engineering, marketing and economics.