讲座题目：Simultaneous variable selection and class fusion with penalized distance criterion based classifiers

主讲人：王启华教授  浙江工商大学

讲座时间：2019年2月28日（星期四）14:00-15:30

讲座地点：综合楼615会议室

主讲人简介：王启华（Wang Qi-hua），研究员，博士生导师，国家杰出青年基金获得者，教育部长江学者奖励计划特聘教授，中国科学院“百人计划”入选者。Elected member of the International Statistical Institute (ISI)。曾到香港、美国、加拿大、德国、澳大利亚、韩国、台湾等多次进行访问。主讲人研究方向主要包括复杂数据统计分析、生存分析、半--非参数统计、高维数据分析。

讲座摘要： In this paper, we propose two new methods to solve the problem of constructing sparse multiclass classifiers and determining corresponding discriminative variables for each pair of classes simultaneously in the high-dimensional setting. In contrast to many existing multiclass classifiers, which can only select informative variables for classification, we can understand roles of the selected variables in separating particular pairs of classes more profoundly by using different penalties. Different from  Guo (2010, Biostatistics) and Xu et al. (2015, Biometrika), which are based on the separate estimation of the precision matrix and mean vectors, we propose to construct classifiers by estimating products of the precision matrix and mean vectors or all discriminant directions directly with more appropriate penalties. This leads to the use of the distance criterion instead of the log-likelihood used in existing literature. With the proposed methods, we can not only consistently select informative variables for classification but also consistently identify corresponding discriminative variables for each pair of classes.  More importantly, our methods attain asymptotically the optimal misclassification error rate for multiclass classification problems, which is not investigated in Guo (2010) and Xu et al. (2015). Simulations and the real data analysis well demonstrate good performances of our methods in comparison with existing methods.