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Information-theoretic measures such as the entropy, cross-entropy and theKullback-Leibler divergence between two mixture models is a core primitive inmany signal processing tasks. Since the Kullback-Leibler divergence of mixturesprovably does not admit a closed-form formula, it is in practice eitherestimated using costly Monte-Carlo stochastic integration, approximated, orbounded using various techniques. We present a fast and generic method thatbuilds algorithmically closed-form lower and upper bounds on the entropy, thecross-entropy and the Kullback-Leibler divergence of mixtures. We illustratethe versatile method by reporting on our experiments for approximating theKullback-Leibler divergence between univariate exponential mixtures, Gaussianmixtures, Rayleigh mixtures, and Gamma mixtures.

Guaranteed bounds on the Kullback-Leibler divergence of univariate mixtures using piecewise log-sum-exp inequalities