Affine Calculus for Constrained Minima of the Kullback–Leibler Divergence

Giovanni Pistone ()
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Giovanni Pistone: De Castro Statistics, Collegio Carlo Alberto, 10122 Torino, Italy

Stats, 2025, vol. 8, issue 2, 1-19

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.

Keywords: information geometry; Kullback–Leibler divergence; statistical bundle; natural gradient (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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