On a problem about I-projections

I. Csiszár, L. Finesso

Research output: Contribution to journalArticle

Abstract

The minimizer P* of the I-divergence I(P∥Q) for P in a set Π defined by linear constraints is known to he mutually absolutely continuous with Q (P* ≡ Q) providing a P̃ in Π exists with P̃ ≡ Q and I(P̃∥Q) < ∞. We ask when the existence of P̄ and P, both in Π, with P̄ Q and I(P∥Q) < ∞ is already sufficient for P* ≡ Q. We give a positive answer for measures on a product space when Π is determined by prescribing the two marginals.

Original languageEnglish
Pages (from-to)41-50
Number of pages10
JournalStudia Scientiarum Mathematicarum Hungarica
Volume34
Issue number1-3
Publication statusPublished - Dec 1 1998

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Keywords

  • I-divergence
  • Iterative scaling
  • Schrödinger's problem
  • Specified marginals

ASJC Scopus subject areas

  • Mathematics(all)

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