On the existence and characterization of the maxent distribution under general moment inequality constraints

Prakash Ishwar, Pierre Moulin

Research output: Contribution to journalArticle

Abstract

A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on the minimum cross-entropy distribution or apply only to distributions with a bounded-volume support or address only equality constraints. The results of this work hold for general moment inequality constraints for probability distributions with possibly unbounded support, and the technical conditions are explicitly on the underlying generalized moment functions. An analytical characterization of the maxent distribution is also derived using results from the theory of constrained optimization in infinite-dimensional normed linear spaces. Several auxiliary results of independent interest pertaining to certain properties of convex coercive functions are also presented.

Original languageEnglish (US)
Pages (from-to)3322-3333
Number of pages12
JournalIEEE Transactions on Information Theory
Volume51
Issue number9
DOIs
StatePublished - Sep 1 2005

Keywords

  • Coercive functions
  • Constrained optimization
  • Convex analysis
  • Cross-entropy
  • Differential entropy
  • Maximum entropy methods

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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