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Affine Calculus for Constrained Minima of the Kullback–Leibler Divergence

Author

Listed:
  • Giovanni Pistone

    (De Castro Statistics, Collegio Carlo Alberto, 10122 Torino, Italy
    Nuovo SEFIR, c/o Coworld, Centro Direzionale Milano Due, Palazzo Canova, 20054 Segrate, Italy)

Abstract

The non-parametric version of Amari’s dually affine Information Geometry provides a practical calculus to perform computations of interest in statistical machine learning. The method uses the notion of a statistical bundle, a mathematical structure that includes both probability densities and random variables to capture the spirit of Fisherian statistics. We focus on computations involving a constrained minimization of the Kullback–Leibler divergence. We show how to obtain neat and principled versions of known computations in applications such as mean-field approximation, adversarial generative models, and variational Bayes.

Suggested Citation

  • Giovanni Pistone, 2025. "Affine Calculus for Constrained Minima of the Kullback–Leibler Divergence," Stats, MDPI, vol. 8(2), pages 1-19, March.
  • Handle: RePEc:gam:jstats:v:8:y:2025:i:2:p:25-:d:1617656
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