Journal
ENTROPY
Volume 18, Issue 12, Pages -Publisher
MDPI
DOI: 10.3390/e18120442
Keywords
information geometry; mixture models; alpha-divergences; log-sum-exp bounds
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Information-theoretic measures, such as the entropy, the cross-entropy and the Kullback-Leibler divergence between two mixture models, are core primitives in many signal processing tasks. Since the Kullback-Leibler divergence of mixtures provably does not admit a closed-form formula, it is in practice either estimated using costly Monte Carlo stochastic integration, approximated or bounded using various techniques. We present a fast and generic method that builds algorithmically closed-form lower and upper bounds on the entropy, the cross-entropy, the Kullback-Leibler and the alpha-divergences of mixtures. We illustrate the versatile method by reporting our experiments for approximating the Kullback-Leibler and the alpha-divergences between univariate exponential mixtures, Gaussian mixtures, Rayleigh mixtures and Gamma mixtures.
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