2 citations · 3 across the 11 of their papers we have counts for
6 papers · 1 filter
Dual-connection midpoint matrix means and their Gauss composition
Frank Nielsen, Kazuki Okamura
Nakamura [J. Comput. Appl. Math. 131 (2001)] proved that the arithmetic--harmonic matrix iteration converges quadratically to the geometric matrix mean, the Riemannian midpoint of…
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…