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Rényi Entropy Power Inequalities via Normal Transport and Rotation

Olivier Rioul 1, 2
1 COMNUM - Communications Numériques
LTCI - Laboratoire Traitement et Communication de l'Information
Abstract : Following a recent proof of Shannon’s entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi entropy is presented that uses transport arguments from normal densities and a change of variable by rotation. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.
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Olivier Rioul. Rényi Entropy Power Inequalities via Normal Transport and Rotation. Entropy, MDPI, 2018, 20 (9), pp.641. ⟨hal-02287964⟩

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