256 citations · 2.3k across the 100 of their papers we have counts for
107 papers
Minimum enclosing Bregman balls made easy
Frank Nielsen
In this work, we revisit the problem of computing minimum enclosing Bregman balls (Bregman MEBs) of finite sets of parameters. First, we show that Bregman MEBs are equivalent to ME…
Fisher-Rao distance and pullback SPD cone distances between multivariate normal distributions
Frank Nielsen
Data sets of multivariate normal distributions abound in many scientific areas like diffusion tensor imaging, structure tensor computer vision, radar signal processing, machine lea…
A numerical approximation method for the Fisher-Rao distance between multivariate normal distributions
Frank Nielsen
We present a simple method to approximate Rao's distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating Rao's…
Product Jacobi-Theta Boltzmann machines with score matching
Andrea Pasquale, Daniel Krefl, Stefano Carrazza +1
The estimation of probability density functions is a non trivial task that over the last years has been tackled with machine learning techniques. Successful applications can be obt…
Simplifying Momentum-based Positive-definite Submanifold Optimization with Applications to Deep Learning
Wu Lin, Valentin Duruisseaux, Melvin Leok +3
Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult di…
Beyond scalar quasi-arithmetic means: Quasi-arithmetic averages and quasi-arithmetic mixtures in information geometry
Frank Nielsen
We generalize quasi-arithmetic means beyond scalars by considering the gradient map of a Legendre type real-valued function. The gradient map of a Legendre type function is proven…