Kernel methods and uncertainty quantification in high-dimensional and structured settings

Aretha Teckentrup (University of Edinburgh)

Wednesday 29th April 12:00-13:00
Maths 311B

Abstract

Kernel methods, in the form of radial basis function interpolation and Gaussian process regression, have proved remarkably successful as a tool for various tasks in approximation and inference. This talk will focus on presenting recent advances in the design and analysis of kernel methods in the context of modern applications, which typically involve very high dimensions as well as complex structures. To combat the challenge of high dimensions, we introduce anisotropic kernels and length-scale informed sparse grids that allow for efficient computations and accurate reconstructions also in this setting. For problems with rapid regime changes, we present non-stationary kernels that are able to faithfully capture the structure and build this into the approximation. 

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