题 目：An efficient tensor regression for high-dimensional data
时 间：2022年10月20日（周四） 10：00-11：00
地 点：线上，Zoom会议，会议号：88132259167，密码：352453
报告人：李国栋 香港大学教授
主持人：王小舟 助理教授
主 办：统计学院
摘 要：
Distributed estimation based on different sources of observations has drawn attention in the modern statistical learning. In practice, due to the expensive cost or time-consuming process to collect data in some cases, the sample size on each local site can be small, but the dimension of covariates is large and may be far larger than the sample size on each site. In this paper, we focus on the distributed estimation and inference for a pre-conceived low-dimensional parameter vector in the high-dimensional quantile regression model with small local sample size. Specifically, we consider that the data are inherently distributed and propose two communication-efficient estimators by generalizing the decorrelated score approach to conquer the slow convergence rate of nuisance parameter estimation and adopting the smoothing technique based on multi-round algorithms. The risk bounds and limiting distributions of the proposed estimators are given. The finite sample performance of the proposed estimators is studied through simulations and an application to a gene expression dataset is also presented.
报告人简介：
李国栋，本科和硕士毕业于北大数学学院，2007年于香港大学统计精算系获得统计学博士，随后在南洋理工大学任助理教授。现任香港大学统计精算系教授。主要研究方向包括时间序列分析，分位数回归，高维统计数据分析和机器学习。李教授目前发表学术论文40余篇，其中10余篇发表在统计学4大顶级期刊，以及机器学习的顶级会议上。题 目：Exact Lowest Rank Recovery of Incomplete Matrices
题 目：Exact Lowest Rank Recovery of Incomplete Matrices
时 间：2022年10月21日（周五） 14：00-15：00
地 点：线上，腾讯会议，会议号：194278539
报告人：王学钦 中国科学技术⼤学教授
主持人：刘玉坤 教授
主 办：统计学院
摘 要：
Many disciplines of research, including statistics, mathematics, and machine learning, have made extensive use of investigated low-rank approximation approaches. As a measure of how well a model fits the data, rank plays an important role in this approach. Its determination is therefore crucial. A number of works in the literature have offered their estimation methods for the fully observed data, but no works address this topic for missing data, which are highly prevalent in real-world applications, in literature. To restore the rank, we present an optimization framework and a method for solving the optimization issue. The unique rank of the underlying matrix can be recovered from the observed incomplete matrix by providing a suitable low-size bound on the observed entries under a simple entry missing mechanism. We also get the Eckart-Young-Mirsky theorem for incomplete matrices as a natural consequence. Several numerical tests and real data analysis demonstrate the efficacy of our strategy.
报告人简介：
王学钦，中国科学技术⼤学讲席教授。2003年毕业于纽约州⽴⼤学宾厄姆顿分校。他现担任中国现场统计研究会副理事⻓，教育部⾼等学校统计学类专业教学指导委员会委员、统计学国际期刊《JASA》等的Associate Editor、高等教育出版社《Lecture Notes: Data Science, Statistics and Probability》系列丛书的副主编。