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

Towards a Canonical Divergence within Information Geometry

Domenico Felice and Nihat Ay


In Riemannian Geometry geodesics are integral curves of the gradient of Riemannian distance. We extend this classical result to the framework of Information Geometry. In particular, we prove that the rays of level-sets defined by a pseudo-distance are generated by the sum of two tangent vectors. By relying on these vectors, we propose a novel definition of divergence and its dual function. We prove that the new divergence defines a dual structure $(g,\nabla,\nabla^*)$ of a statistical manifold M. Additionally, we show that this divergence reduces to the canonical divergence proposed by Ay and Amari in the case of: (a) self-duality, (b) dual flatness, (c) statistical geometric analogue of the concept of symmetric spaces in Riemannian Geometry. The case (c) leads to a further comparison of the novel divergence with the one introduced by Henmi and Kobayashi.


Related publications

2021 Repository Open Access
Domenico Felice and Nihat Ay

Towards a canonical divergence within information geometry

In: Information geometry, 4 (2021) 1, pp. 65-130