The Many Faces of Information Geometry
Abstrak
Information geometry [Ama16, AJLS17, Ama21] aims at unravelling the geometric structures of families of probability distributions and at studying their uses in information sciences. Information sciences is an umbrella term regrouping statistics, information theory, signal processing, machine learning and AI, etc. Information geometry was born independently from econometrician H. Hotelling (1930) and statistician C. R. Rao (1945) from the mathematical curiosity of considering a parametric family of probability distributions, called the statistical model, as a Riemannian manifold equipped with the Fisher metric tensor [Nie20]. Information geometry tackles problems by using the concepts of differential geometry (like curvature) with tensor calculus. In his pioneer work, Rao considered the Riemannian geodesic distance and geodesic balls on the manifold to study classification and hypothesis testing problems in statistics. Let (X,F, μ) denote a probability space [Kee10] (with sample space X, σ-algebra F, and finite positive measure
Penulis (1)
F. Nielsen
Akses Cepat
- Tahun Terbit
- 2022
- Bahasa
- en
- Total Sitasi
- 37×
- Sumber Database
- Semantic Scholar
- DOI
- 10.1090/noti2403
- Akses
- Open Access ✓