Abstract
We define a metric and a family of \(\alpha \)-connections in statistical manifolds, based on \(\varphi \)-divergence, which emerges in the framework of \(\varphi \)-families of probability distributions. This metric and \(\alpha \)-connections generalize the Fisher information metric and Amari’s \(\alpha \)-connections. We also investigate the parallel transport associated with the \(\alpha \)-connection for \(\alpha =1\).
This work was partially funded by CNPq (Proc. 309055/2014-8).
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Vigelis, R.F., de Souza, D.C., Cavalcante, C.C. (2015). New Metric and Connections in Statistical Manifolds. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_25
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DOI: https://doi.org/10.1007/978-3-319-25040-3_25
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