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A correspondence principle for relative entropy minimization

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  • Donald E. Brown
  • Robert L. Smith

Abstract

Relative entropy minimization has been proposed as an inference method for problems with information in the form of constraints on the underlying probability model. We provide a theoretical justification for this procedure through a correspondence principle. In particular, for a convex constraints set Λ, we show that as the number of trials increases, the empirical distribution constrained to lie within Λ and associated with a discrete probability distribution p will become arbitrarily close with high probability to the distribution that minimizes the relative entropy between p and Λ.

Suggested Citation

  • Donald E. Brown & Robert L. Smith, 1990. "A correspondence principle for relative entropy minimization," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(2), pages 191-202, April.
    • Handle: RePEc:wly:navres:v:37:y:1990:i:2:p:191-202
    DOI: 10.1002/1520-6750(199004)37:23.0.CO;2-C
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    References listed on IDEAS

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    1. Allan R. Sampson & Robert L. Smith, 1982. "Assessing Risks Through the Determination of Rare Event Probabilities," Operations Research, INFORMS, vol. 30(5), pages 839-866, October.
    2. John M. Cozzolino & Michael J. Zahner, 1973. "The Maximum-Entropy Distribution of the Future Market Price of a Stock," Operations Research, INFORMS, vol. 21(6), pages 1200-1211, December.
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    Cited by:

    1. Anisha Ghosh & Christian Julliard & Alex P. Taylor, 2017. "What Is the Consumption-CAPM Missing? An Information-Theoretic Framework for the Analysis of Asset Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 30(2), pages 442-504.
    2. Ghosh, Anisha & Julliard, Christian & Taylor, Alex, 2016. "An information based one-factor asset pricing model," LSE Research Online Documents on Economics 118978, London School of Economics and Political Science, LSE Library.

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