New theory sharpens Gaussian Process kernel estimation asymptotics

This paper provides a comprehensive asymptotic theory for the maximum likelihood estimators (MLEs) of Gaussian Process (GP) kernel parameters, specifically focusing on the radial basis function (RBF) kernel. Researchers have commonly used MLEs for kernel parameter estimation in GPs, which are applied across various fields like machine learning, spatial statistics, and time series analysis. However, the asymptotic behavior of these estimators has been largely uncharacterized, particularly under fixed-domain asymptotics due to complex dependencies among observations and nonlinearities in the covariance matrix. The study establishes consistency, derives convergence rates, and proves joint asymptotic normality for the spatial variance, lengthscale, and nugget variance parameters, demonstrating that these rates are minimax optimal. AI

IMPACT Provides theoretical grounding for improving the accuracy and understanding of Gaussian Process models, widely used in machine learning applications.

RANK_REASON Academic paper detailing theoretical advancements in statistical methods for Gaussian Processes. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

• arXiv
• Gaussian Processes
• machine learning
• radial basis function

• paper
• model release

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