Abstract
We study the homogeneous extension of the Kullback-Leibler divergence associated to a covariant variational problem on the statistical bundle. We assume a finite sample space. We show how such a divergence can be interpreted as a Finsler metric on an extended statistical bundle, where the time and the time score are understood as extra random functions defining the model—-. We find a relation between the homogeneous generalisation of the Kullback-Leibler divergence and the Rényi relative entropy, the Rényi parameter being related to the time-reparametrization lapse of the Lagrangian model. We investigate such intriguing relation with an eye to applications in physics and quantum information theory.
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Chirco, G.: In preparation
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The author would like to thank G. Pistone and the anonymous referees for the careful read of the manuscript and the interesting points raised.
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Chirco, G. (2021). Rényi Relative Entropy from Homogeneous Kullback-Leibler Divergence Lagrangian. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham. https://doi.org/10.1007/978-3-030-80209-7_80
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