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This chapter presents fundamentals of Gaussian Process (GP) modeling, starting from the definitions of the GP mean and covariance kernel functions, introducing GP regression equations and then discussing the role and interpretation of GP hyperparameters. Section 2.4 then explores the kernel smoothing perspective, presenting a distilled theory of Reproducing Kernel Hilbert Spaces (RKHS) and connecting GPs to RKHS and to Kernel Ridge Regression. The Chapter includes an online supplement—a Python Jupyter notebook that reproduces two case studies of GP regression on a synthetic univariate response function.

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Gaussian Process Preliminaries

  • 章节

  • 发表日期：

    2025年

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  • Michael Ludkovski,
  • Jimmy Risk

摘要

This chapter presents fundamentals of Gaussian Process (GP) modeling, starting from the definitions of the GP mean and covariance kernel functions, introducing GP regression equations and then discussing the role and interpretation of GP hyperparameters. Section 2.4 then explores the kernel smoothing perspective, presenting a distilled theory of Reproducing Kernel Hilbert Spaces (RKHS) and connecting GPs to RKHS and to Kernel Ridge Regression. The Chapter includes an online supplement—a Python Jupyter notebook that reproduces two case studies of GP regression on a synthetic univariate response function.