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清华大学 邓柯副教授: Bayesian Sufficient Dimension Reduction via Modeling Joint Distributions

光华讲坛——社会名流与企业家论坛第5300期

主题:Bayesian Sufficient Dimension Reduction via Modeling Joint Distributions

主讲人:清华大学 邓柯副教授

主持人:统计学院 林华珍教授

时间:2019年4月25日(星期四)下午4:00-5:00

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:

邓柯博士2008年获得北京大学统计学博士学位,同年进入哈佛大学统计系从事研究工作,历任博士后、副研究员。2013年加入清华大学丘成桐数学科学中心任助理教授。2015年6月,清华大学成立统计学研究中心,统筹清华大学统计学学科的建设,邓柯博士作为创始成员加入统计学研究中心并担任副主任;2016年12月晋升副教授。邓柯博士的研究兴趣包括统计建模、统计计算、生物信息、文本分析、计算机网络透视等领域。他2014年入选“青年千人计划”并当选中国数学会概率统计学会第十届理事会理事,2015年当选中国医疗保健国际交流促进会医学数据与医学计量分会常务委员,2017年当选中国现场统计研究会计算统计分会首任理事长、中国现场统计研究会环境与资源分会常务理事,2018年当选国际计算统计学会亚太地区分会理事(Board Member of IASC-ARS)。他还获得了“2016科学中国人年度人物”的荣誉称号。

主要内容:

Supervised dimension reduction is a classic but still active research topic in statistics, whose goal is to discover a few linear combinations of a large number of predictors (called index variables) that contain all predictive information of the predictors to a response variable. Although many efforts have been given to this classic problem, these methods suffer from either inaccurate estimate, or lack of probabilistic interpretation, or strong technical assumptions. In this paper, we propose a novel Bayesian framework to tackle this classic but still challenging problem. Treating the unknown central subspace as a parameter, and approximate the joint distribution of the response variable and the index variables via nonparametric Bayesian approaches, we come up with a posterior distribution of the unknown central subspace. We show that the obtained posterior distribution converges to the truth when the sample size goes to infinity, and design efficient MCMC algorithms to sample the posterior distribution. Simulation studies confirmed that BSDR can give accurate estimate of the underlying central subspace, support us to do rich inference through the posterior distribution obtained. We also find that the sparsity of indices can be easily achieved by BSDR with an informative prior of the central subspace. These discoveries not only greatly improve our theoretical understanding for SDR, but also provide us powerful tools for practical use.