Rioul, O. Rényi Entropy Power Inequalities via Normal Transport and Rotation. Entropy2018, 20, 641.
Rioul, O. Rényi Entropy Power Inequalities via Normal Transport and Rotation. Entropy 2018, 20, 641.
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.
Rényi entropy; entropy power inequalities; transportation arguments; normal distributions; escort distributions; log-concave distributions
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