报告题目：Two topics in learning with kernels

报 告 人：张海樟教授  中山大学

报告时间：2020年9月17日上午 9:25-10:00

报告地点：腾讯会议 ID：206 372 412

会议密码：0917

校内联系人：王蕊  rwang11@jlu.edu.cn

报告摘要：

We report two pieces of our recent work on learning with kernels: admissible kernels for RKHS embedding of probability distributions, and margin error bounds for the SVM on Banach spaces. These are joint with my PhD student Liangzhi Chen.

Similarity measurement of two probability distributions is important in many applications of statistics. Embedding such distributions into a reproducing kernel Hilbert space (RKHS) has many favorable properties. The choice of the reproducing kernel is crucial in the approach. So far, studies in the literature have been focusing on characteristic kernels which ensure the embedding to yield a metric. We attempt to impose a sophisticated admissible criterion on the reproducing kernel in measuring the similarity of a class of probability distributions.

Support vector machines, which maximize the margin from patterns to the separation hyper-plane subject to correct classifification, have received remarkable success in machine learning. Recently, there have been much interest in developing large margin classifification in Banach spaces. We establish a margin error bound for the SVM on reproducing kernel Banach spaces, thus supplying statistical justifification for pursuing large margin classifification in Banach spaces.

报告人简介：

张海樟，中山大学教授。2003年本科毕业于北京师范大学数学系，2006年硕士毕业于中科院数学所，2009年博士毕业于美国雪城大学（Syracuse University）数学系，2009年6月-2010年5月 密歇根大学（University of Michigan）博士后。2010年6月起担任中山大学教授、博士生导师。主要的研究兴趣为应用调和分析与学习理论，在JMLR, ACHA, J. Complexity等发表专业论文三十余篇，代表性的工作为再生核巴拿赫空间理论和时频分析的Bedrosian恒等式。其与密西根大学Jun Zhang教授合作的基于再生核巴拿赫空间的分类理论入选 Cambridge University Press出版的《数学心理学新手册》。主持国家自然科学基金四项，其中面上项目两项、优秀青年基金一项。