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Seminar on Control Theory and Nonlinear Filtering
Learning "best" kernels from data in Gaussian process regression. With application to aerodynamics
Learning "best" kernels from data in Gaussian process regression. With application to aerodynamics
Organizer
Speaker
Time
Monday, June 26, 2023 3:00 PM - 3:30 PM
Venue
数学系理科楼A-203
Abstract
In this talk, I will introduce algorithms to select/design kernels in Gaussian process regression/kriging surrogate modeling techniques. The authors adopt the setting of kernel method solutions in ad hoc functional spaces, namely Reproducing Kernel Hilbert Spaces (RKHS), to solve the problem of approximating a regular target function given observations of it, i.e. supervised learning. A first class of algorithms is kernel flow, which was introduced in the context of classification in machine learning. It can be seen as a cross-validation procedure whereby a "best" kernel is selected such that the loss of accuracy incurred by removing some part of the dataset (typically half of it) is minimized. A second class of algorithms is called spectral kernel ridge regression, and aims at selecting a "best" kernel such that the norm of the function to be approximated is minimal in the associated RKHS. Within Mercers theorem framework, we obtain an explicit construction of that "best" kernel in terms of the main features of the target function.