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Quantitative Stability of the Entropy Power Inequality.
- Source :
- IEEE Transactions on Information Theory; Aug2018, Vol. 64 Issue 8, p5691-5703, 13p
- Publication Year :
- 2018
-
Abstract
- We establish quantitative stability results for the entropy power inequality (EPI). Specifically, we show that if uniformly log-concave densities nearly saturate the EPI, then they must be close to Gaussian densities in the quadratic Kantorovich-Wasserstein distance. Furthermore, if one of the densities is Gaussian and the other is log-concave, or more generally has positive spectral gap, then the deficit in the EPI can be controlled in terms of the $L^{1}$ -Kantorovich-Wasserstein distance or relative entropy, respectively. As a counterpoint, an example shows that the EPI can be unstable with respect to the quadratic Kantorovich-Wasserstein distance when densities are uniformly log-concave on sets of measure arbitrarily close to one. Our stability results can be extended to non-log-concave densities, provided certain regularity conditions are met. The proofs are based on mass transportation. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 64
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 130667075
- Full Text :
- https://doi.org/10.1109/TIT.2018.2808161