报告题目：高维张量估计与聚类模型

英文题目：Jointly Modeling and Clustering Tensors in High Dimensions

报 告 人:  Biao Cai

报告时间: 12月15日星期五 4:30-5:30

报告地点: 综合楼1001会议室

报告摘要:

      In this talk, we focus on the problem of jointly modeling and clustering populations of tensors by introducing a high-dimensional tensor mixture model with heterogeneous covariances. To effectively tackle the high dimensionality of tensor objects, we employ plausible dimension reduction assumptions that exploit the intrinsic structures of tensors such as low-rankness in the mean and separability in the covariance. In estimation we develop an efficient high-dimensional expectation-conditional-maximization (HECM) algorithm that breaks the intractable optimization in the M-step into a sequence of much simpler conditional optimization problems, each of which is convex admits regularization and has closed-form updating formulas, The theoretical analysis is challenged by both the non-convexity in the EM-type estimation and having access to only the solutions of conditional maximizations in the M-step, leading to the notion of dual non-convexity. We demonstrate that the proposed HECM algorithm, with an appropriate initialization, converges geometrically to a neighborhood that is within statistical precision of the true parameter. The efficacy of the proposed method is demonstrated through comparative numerical experiments and an application to a medical study, where our proposal achieves an improved clustering accuracy over existing benchmarking methods.

报告人简介: 

      Biao Cai is an Assistant Professor in the Department of Mathematical Sciences at University of Cincinnati. Before joining University of Cincinnati, he was a doctoral associate of Yale University. He received his PhD degree in Management Science from University of Miami and his Bachelor’s degree in Statistics from University of Science and Technology of China. His research interests include high dimensional data analysis, point processes, tensor data analysis, multiomics and single cell data analysis. His work has appeared in leading journals such as Journal of the American Statistical Association, Nature Communications. He also received invited review from Operations Research, Journal of the American Statistical Association, Annals of Applied Statistics.