[Celebration Lecture] Zhengjun Zhang：Max-linear Regression Models and Max-linear Logistic Regression Classifier
Time: 11:00-12:00am, Oct. 6th, 2021, Wednesday
Venue: ZOOM（ID：81302052167；password：388334）
Spreker: Zhengjun Zhang, Professor, University of Wisconsin
Abstract:This talk introduces max-linear regression models (Max-LR) and max-linear logistic regression classifiers (Max-logistic) to take advantages of easy interpretable features embedded in linear regression models. It can be seen that linear relation is a special case of max-linear relation. We develop an EM algorithm based maximum likelihood estimation procedure in Max-LR. The consistency and asymptotics of the estimators for parameters are proved. To advance max-linear models to deal with high dimensional predictors, we adopt the common strategy of regularization in the high dimensional regression literature. For Max-logistic,a new type of penalization will be introduced. We demonstrate the broad applicability of max-linear models using simulation examples and real applications in econometric, business modeling, Covid-19 and cancer critical gene detections and disease subtype classifications. The results, in terms of predictability, show a significant improvement compared with solely using regular regression models and other existing machine learning methods. The results enhance our understanding of the relationship between the response variable and the predictors, and among the predictors as well. (Joint work with Qiurong Cui, Yuqing Xu, Vincent Chan).
Speaker’s Bio:张正军教授是美国威斯康辛大学计算机科学、信息、数据科学学院正教授，国际数理统计学院会士和执行委员会委员，美国统计学会会士，担任多个国际经济统计期刊的特刊主编和副主编。主要研究方向包括：极值理论、金融时间序列、金融风险、基于汇率的数字货币、非线性因果推断、稀有事件概率建模、极端气候问题、医学统计中的关键癌症基因识别。
