Information Geometry and Its Applications
published: Dec. 5, 2008, recorded: November 2008, views: 4736
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Information geometry emerged from studies on invariant properties of a manifold of probability distributions. It includes convex analysis and its duality as a special but important part. Here, we begin with a convex function, and construct a dually flat manifold. The manifold possesses a Riemannian metric, two types of geodesics, and a divergence function. The generalized Pythagorean theorem and dual projections theorem are derived therefrom.We construct alpha-geometry, extending this convex analysis. In this review, geometry of a manifold of probability distributions is then given, and a plenty of applications are touched upon. Appendix presents an easily understable introduction to differential geometry and its duality.
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