Convergence of Gaussian process regression: Optimality, robustness, and relationship with kernel ridge regression

2021/04/20 by Wenjia Wang, Bing‐Yi Jing, Wang, Wenjia +1
Biochemistry, Genetics and Molecular Biology · Computer Science · #Advanced Multi-Objective Optimization Algorithms #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Spectroscopy Techniques in Biomedical and Chemical Research #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2104.09778

openalex publication_date 2021/04/20 · openalex created_date 2021/04/26 · openalex updated_date 2026/07/28

Abstract

In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The optimal convergence rate can be attained even if the smoothness of the imposed correlation function exceeds that of the true correlation function and the sampling scheme is quasi-uniform. As byproducts, we also obtain convergence rates of kernel ridge regression with misspecified kernel function, where the underlying truth is a deterministic function. The convergence rates of Gaussian process regression and kernel ridge regression are closely connected, which is aligned with the relationship between sample paths of Gaussian process and the corresponding reproducing kernel Hilbert space.

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