Statistical manifolds and affine differential geometry

摘要

In this paper, we give a summary of geometry of statistical man-ifolds, and discuss relations between information geometry and affine differential geometry. Dually flat spaces and canonical divergence func-tions are important objects in information geometry. We show that such objects can be generalized in the framework of affine differential geometry.In addition, we give a brief summary of geometry of statistical manifolds admitting torsion, which is regarded as a quantum version of statistical manifolds. We discuss relations between statistical manifolds admitting torsion and geometry of affine distributions.