Amari’s Alpha-Geometry
-
Expanding the Geometry of Information
- From Fisher Information to Information Geometry: Outline how Fisher Information metric contributes to the foundation of information geometry, which studies the differential geometric structure of statistical manifolds.
- Alpha-Geometry: Introduction to Shun-ichi Amari’s concept of Alpha-Geometry, which generalizes information geometry by introducing a family of dual connections on statistical Manifolds, parameterized by α.
-
Dualistic Structure and Alpha-Families
- Dual Connections and Divergence: Explain the concept of dual affine connections in the context of Alpha-Geometry and how they lead to a dualistic structure on statistical manifolds, characterizing divergence functions.
- Alpha-Families of Distributions: Discuss how different values of α result in different geometrical structures (e.g., the Fisher metric at α=0, and Dual Geometries at α=±1), and their implications for understanding the geometry of statistical models.
See Also: