Posterior contraction for deep Gaussian process priors

TL;DR

This paper establishes that deep Gaussian process priors can achieve near-minimax contraction rates in nonparametric regression, adapting to the function's structure and smoothness, thus extending Bayesian nonparametric theory.

Contribution

It introduces a framework demonstrating that deep Gaussian process priors attain optimal contraction rates while adapting to underlying function properties.

Findings

Achieves near-minimax convergence rates with deep Gaussian process priors.

Provides a theoretical foundation extending Bayesian nonparametric results.

Demonstrates adaptivity to function structure and smoothness.

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.