Dimension-free log-Sobolev inequalities for mixture distributions
| Autor: | Hong-Bin Chen, Jonathan Niles-Weed, Sinho Chewi |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics::Functional Analysis
Conjecture Probability (math.PR) Mathematics::Analysis of PDEs Functional Analysis (math.FA) Sobolev inequality Mathematics - Functional Analysis Combinatorics Distribution (mathematics) Mixing (mathematics) Bounded function FOS: Mathematics Uniform boundedness Mixture distribution Mathematics - Probability Analysis Mathematics Probability measure |
| Zdroj: | Journal of Functional Analysis. 281:109236 |
| ISSN: | 0022-1236 |
| Popis: | We prove that if ${(P_x)}_{x\in \mathscr X}$ is a family of probability measures which satisfy the log-Sobolev inequality and whose pairwise chi-squared divergences are uniformly bounded, and $\mu$ is any mixing distribution on $\mathscr X$, then the mixture $\int P_x \, \mathrm{d} \mu(x)$ satisfies a log-Sobolev inequality. In various settings of interest, the resulting log-Sobolev constant is dimension-free. In particular, our result implies a conjecture of Zimmermann and Bardet et al. that Gaussian convolutions of measures with bounded support enjoy dimension-free log-Sobolev inequalities. Comment: 16 pages |
| Databáze: | OpenAIRE |
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