A Quantitative Entropy Power Inequality for Dependent Random Vectors

Mokshay Madiman; James Melbourne; Cyril Roberto

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arXiv · 2512.19002

A Quantitative Entropy Power Inequality for Dependent Random Vectors

Mokshay Madiman·James Melbourne·Cyril Roberto

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Abstract

The entropy power inequality for independent random vectors is a foundational result of information theory, with deep connections to probability and geometric functional analysis. Several extensions of the entropy power inequality have been developed for settings with dependence, including by Takano, Johnson, and Rioul. We extend these works by developing a quantitative version of the entropy power inequality for dependent random vectors. A notable consequence is that an entropy power inequality stated using conditional entropies holds for random vectors whose joint density is log-supermodular.

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Mokshay Madiman, James Melbourne, Cyril Roberto. 2025-12-22. A Quantitative Entropy Power Inequality for Dependent Random Vectors. https://arxiv.org/abs/2512.19002

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