A Novel Approach to Canonical Divergences within Information Geometry

Entropy

Nihat Ay¹  Shun-ichi Amari² 

[1] Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, Leipzig 04103 , GermanyLaboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Wako-shi Hirosawa 2-1, Saitama 351-0198, Japan;

关键词: information geometry;    canonical divergence;    relative entropy;    α-divergence;    α-geodesic;    duality;    geodesic projection;   

DOI  :  10.3390/e17127866

来源: mdpi

【 摘 要 】

A divergence function on a manifold M defines a Riemannian metric g and dually coupled affine connections ∇ and . We propose a natural definition of a canonical divergence for a general, not necessarily flat, M by using the geodesic integration of the inverse exponential map. The new definition of a canonical divergence reduces to the known canonical divergence in the case of dual flatness. Finally, we show that the integrability of the inverse exponential map implies the geodesic projection property.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.