A Quantitative Entropy Power Inequality for Dependent Random Vectors

2025/12/22 by Mokshay Madiman, Madiman, Mokshay, James Melbourne +3
Decision Sciences · Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Mathematical Inequalities and Applications #Probability (math.PR) #Risk and Portfolio Optimization #Wireless Communication Security Techniques

paper · doi:10.48550/arxiv.2512.19002

openalex publication_date 2025/12/22 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28

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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Related

• A conditional Entropy Power Inequality for dependent variables
• Unifying the Brascamp-Lieb Inequality and the Entropy Power Inequality
• Entropy-power inequality for weighted entropy
• A new entropy power inequality for integer-valued random variables
• Yet Another Proof of the Entropy Power Inequality