Beyond the Entropy Power Inequality, via Rearrangements

Wang L.; Madiman M.

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Beyond the Entropy Power Inequality, via Rearrangements

机译：通过重排超越了熵幂不等式

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摘要

A lower bound on the Rényi differential entropy of a sum of independent random vectors is demonstrated in terms of rearrangements. For the special case of Boltzmann–Shannon entropy, this lower bound is better than that given by the entropy power inequality. Several applications are discussed, including a new proof of the classical entropy power inequality and an entropy inequality involving symmetrization of Lévy processes.

机译：就重排而言，证明了独立随机向量之和的Rényi微分熵的下界。对于Boltzmann-Shannon熵的特殊情况，该下界比熵幂不等式给出的下界更好。讨论了几种应用，包括经典熵幂不等式的新证明和涉及Lévy过程对称化的熵不等式。

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来源
《Information Theory, IEEE Transactions on》 |2014年第9期|5116-5137|共22页
作者
Wang L.; Madiman M.;
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作者单位

Department of Physics, Yale University, New Haven, CT, USA;

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正文语种 eng
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关键词
Convergence; Convolution; Electronic mail; Entropy; Probability density function; Random variables; Vectors; Entropy power inequality; R??nyi entropy; majorization; spherically symmetric rearrangement;

机译：收敛;卷积;电子邮件;熵;概率密度函数;随机变量;向量;熵幂不等式;R ?? nyi熵;优化;球对称重排;

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2. Entropy Power Inequality for the Rényi Entropy [J] . Bobkov S.G., Chistyakov G.P. Information Theory, IEEE Transactions on . 2015,第2期

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3. Inequalities Related to Rearrangements of Powers and Symmetric Polynomials [J] . Cezar Joita, Pantelimon Stanica Journal of inequalities in pure and applied mathematics . 2003,第2期

机译：与幂和对称多项式的重排有关的不等式
4. A new approach to the entropy power inequality, via rearrangements [C] . Wang Liyao, Madiman Mokshay IEEE International Symposium on Information Theory . 2013

机译：通过重新排列来解决熵幂不等式的新方法
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7. Beyond the entropy power inequality, via rearrangements [O] . Wang, Liyao, Madiman, Mokshay 2014

机译：超越熵权不平等，通过重新排列

Beyond the Entropy Power Inequality, via Rearrangements

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