2 citations · 3 across the 11 of their papers we have counts for
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A note on the Artstein-Avidan-Milman's generalized Legendre transforms
Frank Nielsen
Artstein-Avidan and Milman [Annals of mathematics (2009), (169):661-674] characterized invertible reverse-ordering transforms on the space of lower semi-continuous extended real-va…
Fast proxy centers for Jeffreys centroids: The Jeffreys-Fisher-Rao and the inductive Gauss-Bregman centers
Frank Nielsen
The symmetric Kullback-Leibler centroid also called the Jeffreys centroid of a set of mutually absolutely continuous probability distributions on a measure space provides a notion…
Symplectic Bregman divergences
Frank Nielsen
We present a generalization of Bregman divergences in symplectic vector spaces that we term symplectic Bregman divergences. Symplectic Bregman divergences are derived from a symple…
Divergences induced by dual subtractive and divisive normalizations of exponential families and their convex deformations
Frank Nielsen
Exponential families are statistical models which are the workhorses in statistics, information theory, and machine learning among others. An exponential family can either be norma…