Toni Karvonen (University of Helsinki) - Data Science
Date: May 17th 2023 Location: Eurecom - Eurecom
ABSTRACT: In this talk I discuss some results on maximum likelihood estimation of covariance kernel parameters in Gaussian process interpolation, where Gaussian processes are used to approximate deterministic functions in the absence of noise, and review the effect the kernel and its parameters have on the reliability of the predictive variance as a measure of predictive uncertainty. I focus on the Matérn class of kernels, which is commonly used in machine learning and spatial statistics, and the extent to which maximum likelihood estimation is capable of detecting the smoothness of the latent function. The results rely on connections between Gaussian process interpolation and the theory of optimal approximation in reproducing kernel Hilbert spaces. The talk is primarily based on the following papers:  T. Karvonen, G. Wynne, F. Tronarp, C. J. Oates & S. Särkkä (2020). Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions. SIAM/ASA Journal on Uncertainty Quantification, 8(3):926–958.  T. Karvonen (2023). Asymptotic bounds for smoothness parameter estimates in Gaussian process interpolation. arXiv:2203.05400v3.  T. Karvonen and C. J. Oates (2023). Maximum likelihood estimation in Gaussian process regression is ill-posed. Journal of Machine Learning Research, 24(120):1-47. BIO: Toni Karvonen has been a postdoctoral researcher funded by the Academy of Finland in the Department of Mathematics and Statistics at the University of Helsinki. Prior to this he was a research fellow at the Alan Turing Institute in London. He obtained his doctoral degree, supervised by Simo Särkkä, from the Department of Electrical Engineering and Automation at Aalto University in 2019. His primary research interests are Gaussian process interpolation, approximation and integration in reproducing kernel Hilbert spaces, and probabilistic numerics.