Sharp Asymptotic Theory of Maximum Likelihood Estimation for Gaussian Processes with an RBF Kernel
Gaussian processes (GPs) are widely used across machine learning, spatial statistics, time-series analysis, optimization, Bayesian statistics, and scientific applications.
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Key points
- A central component of a GP model is its kernel, which is typically specified through a parametric family.
- Among the most widely used choices is the radial basis function (RBF), also known as the squared exponential or Gaussian kernel, owing to its simple form, smoothness, and flexibility.
- Despite this widespread use, the asymptotic behavior of the MLEs remains poorly understood under fixed-domain asymptotics, even for the RBF kernel.
- In this paper, we address this gap by providing, to the best of our knowledge, the first complete asymptotic characterization of the joint MLE of the spatial variance, lengthscale, and nugget variance under fixed-domain asymptotics.
Sources (1)
- [1]Sharp Asymptotic Theory of Maximum Likelihood Estimation for Gaussian Processes with an RBF KernelarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 01:44 PM
Gaussian processes (GPs) are widely used across machine learning, spatial statistics, time-series analysis, optimization, Bayesian statistics, and scientific applications.
A central component of a GP model is its kernel, which is typically specified through a parametric family.
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