Towards a Canonical Divergence within Information Geometry

Understand

In Riemannian geometry geodesics are integral curves of the Riemannian distance gradient.

• 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 a canonical divergence and its dual function.