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What is Learnable in Valiant's Theory of the Learnable? 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Quantitative spectral gap estimate and Wasserstein contraction of simple slice sampling
Viacheslav Natarovskii, Daniel Rudolf, Björn Sprungk · 2019-03-10 · via math.ST updates on arXiv.org

We prove Wasserstein contraction of simple slice sampling for approximate sampling w.r.t. distributions with log-concave and rotational invariant Lebesgue densities. This yields, in particular, an explicit quantitative lower bound of the spectral gap of simple slice sampling. Moreover, this lower bound carries over to more general target distributions depending only on the volume of the (super-)level sets of their unnormalized density.

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