An Entropy Power Inequality for Dependent Variables

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IEEE Transactions on Information Theory
The entropy power inequality for independent random variables is a foundational result of information theory, with deep connections to probability and geometric functional analysis. Very few extensions of the entropy power inequality have been developed for settings with dependence. We address this gap in the literature by developing entropy power inequalities for dependent random variables. In particular, we highlight the role of log-supermodularity in delivering sufficient conditions for an entropy power inequality stated using conditional entropies.
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Entropy Power Inequality, Dependent Variables, log-supermodular, submodular functions, Fisher information
M. Madiman, J. Melbourne and C. Roberto, "An Entropy Power Inequality for Dependent Variables," in IEEE Transactions on Information Theory, doi: 10.1109/TIT.2024.3385728.