We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Information geometry.
- Authors
Amari, Shun-ichi
- Abstract
Information geometry has emerged from the study of the invariant structure in families of probability distributions. This invariance uniquely determines a second-order symmetric tensor g and third-order symmetric tensor T in a manifold of probability distributions. A pair of these tensors (g, T) defines a Riemannian metric and a pair of affine connections which together preserve the metric. Information geometry involves studying a Riemannian manifold having a pair of dual affine connections. Such a structure also arises from an asymmetric divergence function and affine differential geometry. A dually flat Riemannian manifold is particularly useful for various applications, because a generalized Pythagorean theorem and projection theorem hold. The Wasserstein distance gives another important geometry on probability distributions, which is non-invariant but responsible for the metric properties of a sample space. I attempt to construct information geometry of the entropy-regularized Wasserstein distance.
- Subjects
AFFINE geometry; GEOMETRY; RIEMANNIAN metric; RIEMANNIAN manifolds; DISTRIBUTION (Probability theory); PYTHAGOREAN theorem
- Publication
Japanese Journal of Mathematics, 2021, Vol 16, Issue 1, p1
- ISSN
0289-2316
- Publication type
Article
- DOI
10.1007/s11537-020-1920-5