Posterior contraction for deep Gaussian process priors

Gianluca Finocchio; Johannes Schmidt-Hieber

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arXiv · 2105.07410

Posterior contraction for deep Gaussian process priors

Gianluca Finocchio·Johannes Schmidt-Hieber

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Abstract

We study posterior contraction rates for a class of deep Gaussian process priors applied to the nonparametric regression problem under a general composition assumption on the regression function. It is shown that the contraction rates can achieve the minimax convergence rate (up to $\log n$ factors), while being adaptive to the underlying structure and smoothness of the target function. The proposed framework extends the Bayesian nonparametric theory for Gaussian process priors.

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Gianluca Finocchio, Johannes Schmidt-Hieber. 2021-05-16. Posterior contraction for deep Gaussian process priors. https://arxiv.org/abs/2105.07410

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