Invariant Geometry of Manifold of Probability Distributions

  • Shun-ichi Amari
Part of the Applied Mathematical Sciences book series (AMS, volume 194)


We have introduced a dually flat Riemannian structure in the manifolds of the exponential family and the mixture family based on the convexity of the cumulant generating function (free energy) and the negative entropy, respectively. The KL-divergence is derived from these convex functions.


Convex Function Fisher Information Coarse Graining Fisher Information Matrix Riemannian Metrics 
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Copyright information

© Springer Japan 2016

Authors and Affiliations

  1. 1.Brain Science InstituteRIKENWakoJapan

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