Expected Value Minimization in Information Theoretic Multiple Priors Models

I. Csiszár, Thomas Breuer

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Minimization of the expectation EP(X) of a random variable X over a family Γ of plausible prior distributions P is addressed, when Γ is a level set of some convex integral functional. As typical cases, Γ may be an I-divergence ball or some other f-divergence ball or Bregman distance ball. Regarding localization of the infimum we show that whether or not the minimum of EP(X) subject to P∈ Γ is attained, the densities of the almost minimizing distributions cluster around an explicitly specified function that may have integral less than 1 if the minimum is not attained. If Γ is an f-divergence ball of radius k, the minimum is either attained for any choice of k, or it is/is not attained when k is less/larger than a critical value. A conjecture is formulated about extending this result beyond f-divergence balls.

Original languageEnglish
JournalIEEE Transactions on Information Theory
DOIs
Publication statusAccepted/In press - Apr 19 2018

Keywords

  • Bregman distance
  • Convex functions
  • Entropy
  • f-divergence
  • Finance
  • generalized exponential family
  • Information geometry
  • information geometry
  • Mathematical model
  • Minimization
  • Random variables
  • risk measure

ASJC Scopus subject areas

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

Fingerprint Dive into the research topics of 'Expected Value Minimization in Information Theoretic Multiple Priors Models'. Together they form a unique fingerprint.

  • Cite this