On the Kullback-Leibler divergence between discrete normal distributions

Frank Nielsen

doi:10.1007/s41745-021-00279-5

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arXiv · 2109.14920

On the Kullback-Leibler divergence between discrete normal distributions

Frank Nielsen

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Abstract

Discrete normal distributions are defined as the distributions with prescribed means and covariance matrices which maximize entropy on the integer lattice support. The set of discrete normal distributions form an exponential family with cumulant function related to the Riemann theta function. In this paper, we present several formula for common statistical divergences between discrete normal distributions including the Kullback-Leibler divergence. In particular, we describe an efficient approximation technique for calculating the Kullback-Leibler divergence between discrete normal distributions via the R\'enyi $\alpha$-divergences or the projective $\gamma$-divergences.

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Frank Nielsen. 2021-09-30. On the Kullback-Leibler divergence between discrete normal distributions. https://doi.org/10.1007/s41745-021-00279-5

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