- 控制理论和非线性滤波讨论班

Learning "best" kernels from data in Gaussian process regression. With application to aerodynamics

组织者

丘成栋

演讲者

康家熠

时间

2023年06月26日 15:00 至 15:30

地点

数学系理科楼A-203

摘要

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.