Posterior contraction for deep Gaussian process priors

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.

arXiv comment56 pages, 3 figures

References in corpus (5)

• Rates of contraction of posterior distributions based on Gaussian process priors
• Reproducing kernel Hilbert spaces of Gaussian priors
• Random Feature Expansions for Deep Gaussian Processes
• On the Impact of the Activation Function on Deep Neural Networks Training
• Posterior Concentration for Sparse Deep Learning