MEM pixel correlated solutions for generalized moment and interpolation problems

Imre Csiszár, Fabrice Gamboa, Elisabeth Gassiat

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

In generalized moment problems (signed) measures are searched to fit given observations, or continuous functions are searched to fit given constraints. Known convex methods for solving such problems, and their stochastic interpretations via Maximum Entropy on the Mean (MEM) and in a Bayesian sense are reviewed, with some improvements on previous results. Then the MEM and Bayesian approaches are extended to default models with a dependence structure, yielding new families of solutions. One family involves a transfer kernel, and allows using prior information such as modality, convexity, or Sobolev norms. Another family of solutions with possibly nonconvex criteria, is arrived at using default models with exchangeable random variables. The main technical tools are convex analysis and large deviations theory.

Original languageEnglish
Pages (from-to)2253-2270
Number of pages18
JournalIEEE Transactions on Information Theory
Volume45
Issue number7
DOIs
Publication statusPublished - Dec 1 1999

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ASJC Scopus subject areas

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

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