主题：Matrix regression heterogeneity analysis
时间：6月20日 13:30-15:00
地点：腾讯会议：438-014-7163
主持人：姜荣教授
报告人简介：
张三国，现为中国科学院大学数学科学学院教授，2002年毕业于中国科学技术大学，获博士学位。先后于03年8月-04年7月在香港中文大学统计学系，07年2月-08年8月在美国范德堡大学（Vanderbilt University）的医学中心公众健康研究所与生物统计系从事博士后研究工作。多年来一直从事高维数据分析，生物与医学统计、统计机器学习教学科研工作，曾获得2017年中国科学院优秀导师奖。近五年来发表论文三十余篇，相关研究成果发表在Sciences in China-Mathematics, JASA，Bioinformatics, Biometrics等数理统计、生物统计和生物信息学领域的权威期刊。主持多项纵向和横向课题，包括国家自然科学天元基金重点、面上、青年项目，企业和军工科研项目等。
讲座简介：
The development of modern science and technology has facilitated the collection of a large amount of matrix data in fields such as biomedicine. Matrix data modeling has been extensively studied, which advances from the naive approach of flattening the matrix into a vector. However, existing matrix modeling methods mainly focus on homogeneous data, failing to handle the data heterogeneity frequently encountered in the biomedical field, where samples from the same study belong to several underlying subgroups, and different subgroups follow different models. In this paper, we focus on regression-based heterogeneity analysis. We propose a matrix data heterogeneity analysis framework, by combining matrix bilinear sparse decomposition and penalized fusion techniques, which enables data-driven subgroup detection, including determining the number of subgroups and subgrouping membership. A rigorous theoretical analysis is conducted, including asymptotic consistency in terms of subgroup detection, the number of subgroups, and regression coefficients. Numerous numerical studies based on simulated and real data have been constructed, showcasing the superior performance of the proposed method in analyzing matrix heterogeneous data.
