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.
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CITATION STYLE
Vigelis, R. F., De Souza, D. C., & Cavalcante, C. C. (2015). New metric and connections in statistical manifolds. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9389, pp. 222–229). Springer Verlag. https://doi.org/10.1007/978-3-319-25040-3_25
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