MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Affine Natural Proximal Learning

Wuchen Li, Alex Tong Lin and Guido Montúfar


We revisit the natural gradient method for learning in statistical manifolds. We consider the proximal formulation and obtain a closed form approximation of the proximity term over an affine subspace of functions in the Legendre dual formulation. We consider two important types of statistical metrics, namely the Wasserstein and Fisher-Rao metrics, and introduce numerical methods for high dimensional parameter spaces.

optimal transport, information geometry, Proximal operator

Related publications

2019 Repository Open Access
Wuchen Li, Alex Tong Lin and Guido Montúfar

Affine natural proximal learning

In: Geometric science of information : 4th international conference, GSI 2019, Toulouse, France, August 27-29, 2019, proceedings / Frank Nielsen... (eds.)
Cham : Springer, 2019. - pp. 705-714
(Lecture notes in computer science ; 11712)