Posterior Contraction for Deep Gaussian Process Priors

Gianluca Finocchio, Johannes Schmidt-Hieber.

Year: 2023, Volume: 24, Issue: 66, Pages: 1−49


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.