# 学术报告（吕绍高副教授 1.17)

目：Minimax rates for sparse multi-kernelclassification via a new $\ell_1$-based SVM

点：新数学楼415报告厅

要：This talk presents minimax rates ofnonparametric classification under the framework of sparse support vectormachine (SVM) with multiple kernels. The sparse SVM with multiple kernels referto  the setting where  only a relatively small number of kernels are relevant to the response, even if the total number of kernels is very large. We primarily focus on errorbounds for the sparse SVM, and establish sharp oracle inequalities viaproposing a group-type Lasso scheme within the framework of reproducing kernelHilbert spaces. Moreover, we complement our upper bounds by deriving minimaxlower bounds of the relative classification error over multi-kernel class,thereby showing the optimality ofour method. Our theoretical results not onlyprovide unified theoretical results for multi-kernel SVMs, also enrich thedevelopment of high dimensional nonparametric classification in statistics.