New metric and connections in statistical manifolds - Charles Cavalcante, David de Souza, Rui Vigelis

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Authors : Charles Cavalcante, David de Souza, Rui Vigelis
DOI URL : http://dx.doi.org/10.1007/978-3-319-25040-3_25
Video : No Autorisation
Slides : No Autorisation
Presentation : https://www.see.asso.fr/node/14278
Creative Commons Attribution-ShareAlike 4.0 International

Abstract:
We define a metric and a family of α-connections in statistical manifolds, based on ϕ-divergence, which emerges in the framework of ϕ-families of probability distributions. This metric and α-connections generalize the Fisher information metric and Amari’s α-connections. We also investigate the parallel transport associated with the α-connection for α = 1.