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Dimension-free log-Sobolev inequalities for mixture distributions by Chen, Hong-Bin; Chewi, Sinho; Niles-Weed, Jonathan is a scholarly article available to read on EtoBox.

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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.

Author

Chen, Hong-Bin; Chewi, Sinho; Niles-Weed, Jonathan

Published

2021

Language

EN