A Quantitative Entropy Power Inequality for Dependent Random Vectors
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911331767025664 |
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| author | Madiman, Mokshay Melbourne, James Roberto, Cyril |
| author_facet | Madiman, Mokshay Melbourne, James Roberto, Cyril |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19002 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Quantitative Entropy Power Inequality for Dependent Random Vectors Madiman, Mokshay Melbourne, James Roberto, Cyril Information Theory Probability 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. |
| title | A Quantitative Entropy Power Inequality for Dependent Random Vectors |
| topic | Information Theory Probability |
| url | https://arxiv.org/abs/2512.19002 |