8 papers
Group invariance of -divergences and the Fisher--Rao distance
Frank Nielsen, Kazuki Okamura
Many statistical models have natural symmetries described by a group action. We study how such symmetries affect the comparison of two distributions. We work with a transformation…
Neural Legendre-Fenchel transform with Hessian Preconditioning
Basile Plus-Gourdon, Frank Nielsen
The Legendre-Fenchel (LF) transform is a fundamental tool in convex analysis and machine learning that maps lower semi-continuous functions to their convex conjugates. In practice,…
Generalising maximum mean discrepancy: kernelised functional Bregman divergences
Russell Tsuchida, Frank Nielsen
Bregman divergences play a pivotal role in statistics, machine learning and computational information geometry. Particularly in the context of machine learning, they are central to…
Quadratic polarity and polar Fenchel-Young divergences from the canonical Legendre polarity
Frank Nielsen, Basile Plus-Gourdon, Mahito Sugiyama
Polarity is a fundamental reciprocal duality of -dimensional projective geometry which associates to points polar hyperplanes, and more generally -dimensional convex bodies t…
Geometric structures and deviations on James' symmetric positive-definite matrix bicone domain
Jacek Karwowski, Frank Nielsen
Symmetric positive-definite (SPD) matrix datasets play a central role across numerous scientific disciplines, including signal processing, statistics, finance, computer vision, inf…
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…