Posterior Contraction for Deep Gaussian Process Priors

Gianluca Finocchio; Johannes Schmidt-Hieber

We study posterior contraction rates for a class of deep Gaussian process priors in the nonparametric regression setting 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.

Posterior Contraction for Deep Gaussian Process Priors

Abstract