光华讲坛——社会名流与企业家论坛第5478期

主题：Covariate Assisted Principal Regression for Covariance Matrix Outcomes

主讲人：德克萨斯大学 罗曦副教授

主持人：周岭 副教授

时间：2019年7月5日（星期五） 下午16:00-17:00

地点：西南财经大学柳林校区弘远楼408会议室

主办单位：统计研究中心 统计学院 科研处

主讲人简介：

Dr. Xi Luo is a tenured Associate Professor in Department of Biostatistics and Data Science at The University of Texas Health Science Center at Houston.

Dr. Luo has broad expertise in machine learning, network/pathway inference, big data analytics, causal inference, and statistical computing. His research group is currently focusing on developing novel statistical methods for neuroimaging, genetics, and other scientific areas with big and complex data challenges.

Dr. Luo has published more than 30 papers in journals and conference proceedings, including the world’s top journals on Statistics or science. As PI, he has received more than 1 million dollar funding form NIH and NSF since 2015. He has also served as grant reviewers for NIH, NSF, and other funding agencies. In addition, he has worked as members for research award and program committees for several international statistics conferences.

罗曦博士是德克萨斯大学休斯敦健康科学中心生物统计学和数据科学系的终身副教授。

罗博士在机器学习，网络/路径推理，大数据分析，因果推理和统计计算方面拥有广泛的专业知识。 他的研究小组目前专注于开发新型统计方法适用于神经影像学，遗传学和其他具有重大和复杂数据挑战的科学领域。

罗博士在期刊和会议论文集上发表了30多篇论文，其中包括世界顶级的统计学或科学期刊。 作为主研究责任人，自2015年以来，他已经从NIH和NSF获得了超过100万美元的资金。他还曾担任NIH，NSF和其他资助机构的资助审查员。 此外，他还曾担任多个国际统计会议的研究奖励和计划委员会成员。

主要内容：

Modeling variances in data has been an important topic in many fields, including in financial and neuroimaging analysis. We consider the problem of regressing covariance matrices on vector covariates, collected from each observational unit. The main aim of this paper is to uncover the variation in the covariance matrices across units that are explained by the covariates. This paper introduces Covariate Assisted Principal (CAP) regression, an optimizationbased method for identifying the components predicted by (generalized) linear models of the covariates. We develop computationally efficient algorithms to jointly search the linear projections of the covariance matrices as well as the regression coefficients, and we establish the asymptotic properties. Using extensive simulation studies, our method shows higher accuracy and robustness in coefficient estimation than competing methods. Applied to a restingstate functional magnetic resonance imaging study, our approach identifies the human brain network changes associated with age and sex.

协方差矩阵的建模一直是许多领域的重要课题，包括财务和神经影像分析。我们考虑从每个观察单元收集的矢量协变量上的协方差矩阵回归问题。该本文的主要目的是揭示各单元之间协方差矩阵的变化协变量。本文介绍了Covariate Assisted Principal（CAP）回归，一种基于优化的方法的方法识别由协变量的（广义）线性模型预测的分量。我们开发计算效率高算法联合搜索协方差矩阵的线性投影以及回归系数，我们建立渐近性质。通过广泛的模拟研究，我们的方法显示出更高的准确性和鲁棒性系数估计比竞争方法。应用于功能磁共振成像研究，我们的方法确定了与年龄和性别相关的人类大脑网络变化。