Report title: Two topics in Learning with kernels

Reporter: Professor Zhang Haizhang, Sun Yat-Sen University

Reporting time: 9:25-10:00 am, September 17, 2020

Report location: Tencent Conference ID: 206 372 412

Conference password: 0917

School contact: Wang Rui rwang11@jlu.edu.cn

Report summary:

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.

Brief introduction of the speaker:

Zhang Haizhang, professor at Sun Yat-Sen University，graduated from the Department of Mathematics, Beijing Normal University in 2003, the Institute of Mathematics, Chinese Academy of Sciences in 2006, and the Department of Mathematics, Syracuse University, USA in 2009. He was a Postdoc from June 2009 to May 2010, from the University of Michigan. Michigan). Since June 2010, he has been a professor and doctoral supervisor of Sun Yat-Sen University. His main research interest is the application of harmonic analysis and learning theory. He has published more than 30 professional papers in JMLR, ACHA, J. Complexity, etc., and his representative work is the regenerative nuclear Banach space theory and the Bedrosian identity of time-frequency analysis. The classification theory based on the Banach space of reproducing nuclear nucleus, which he collaborated with Professor Jun Zhang of the University of Michigan, was selected into the "New Handbook of Mathematical Psychology" published by Cambridge University Press, and he also presided over four National Natural Science Foundation of China, including two general projects and one outstanding youth fund.