Chentsov's theorem
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In information geometry, Chentsov's theorem states that the Fisher information metric is, up to rescaling, the unique Riemannian metric on a statistical manifold that is invariant under sufficient statistics.
See also[]
References[]
- Dowty, James G. (2018). "Chentsov's theorem for exponential families". Information Geometry. 1 (1): 117-135. arXiv:1701.08895. doi:10.1007/s41884-018-0006-4.
- Shun'ichi Amari, Hiroshi Nagaoka (2000) Methods of information geometry, Translations of mathematical monographs; v. 191, American Mathematical Society.
Categories:
- Differential geometry
- Information geometry
- Statistical distance