主 题：Regularized tensor quantile regression with applications to neuroimaging data analysis

主讲人：阿尔伯塔大学Kong Linglong教授

主持人：统计学院林华珍教授

时间：2022年12月14日（周三）上午9:30-10:30

直播平台及会议ID：腾讯会议，ID:

主办单位：统计研究中心和统计学院 科研处

主讲人简介：

Dr. Linglong Kong is a professor in the Department of Mathematical and Statistical Sciences at the University of Alberta. He holds a Canada Research Chair in Statistical Learning, a Canada CIFAR AI Chair, and is a fellow of the Alberta Machine Intelligence Institute (AMII). His publication record includes more than 70 peer-reviewed articles in top journals such as AOS, JASA and JRSSB as well as top conferences such as NeurIPS, ICML, ICDM, AAAI, and IJCAI. Dr. Kong currently serves as associate editor of the Journal of the American Statistical Association, the Canadian Journal of Statistics, and Statistics and its Interface, as well as guest editor of Statistics and its Interface. Additionally, Dr. Kong is a member of the Executive Committee of the Western North American Region of the International Biometric Society, chair of the ASA Statistical Computing Session program, and chair of the webinar committee. He served as a guest editor of Canadian Journal of Statistics, associate editor of International Journal of Imaging Systems and Technology, guest associate editor of Frontiers of Neurosciences, chair of the ASA Statistical Imaging Session, and member of the Statistics Society of Canada's Board of Directors. He is interested in the analysis of high-dimensional and neuroimaging data, statistical machine learning, robust statistics and quantile regression, as well as artificial intelligence for smart health.

Linglong Kong，阿尔伯塔大学数学与统计科学系教授，加拿大统计学习研究主席，加拿大CIFAR AI主席，阿尔伯塔机器智能研究所(AMII)的研究员。在AOS、JASA和JRSSB等统计学顶级期刊以及NeurIPS、ICML、ICDM、AAAI和IJCAI等顶级会议期刊上发表论文70余篇。他目前担任JASA和Canadian Journal of Statistics副主编，以及Statistics and its Interface的副主编和guest editor。此外，他也是国际生物计量学会北美西部地区执行委员会的成员，ASA统计计算会议项目的主席，网络研讨会委员会的主席。他曾担任Canadian Journal of Statistics的guest editor，International Journal of Imaging Systems and Technology的副主编，Frontiers of Neurosciences的guest associate editor，ASA统计成像会议主席，以及加拿大统计学会董事会成员。他对高维和神经成像数据的分析、统计机器学习、稳健统计和分位数回归以及智能健康的人工智能感兴趣。

内容提要：

Our work develops a regularized tensor quantile regression framework for scalar responses and enables the robust analysis of tensor-variate data. Beyond our presented application to neuroimaging for identifying regions of the hippocampus implicated in Alzheimer's disease, tensor-variate data are ubiquitous in medicine, ecology, and other fields where large volumes of data are collected. The tensor quantile model considered in our work stands separate from previously-established tensor regression frameworks and requires its own theoretical investigation. We establish important statistical properties of our tensor effect estimator and convergence properties of our proposed estimation algorithm. To address the high dimensionality of the tensor quantile model and the non-differentiability of the quantile loss function, we assume that the tensor effect admits a Tucker decomposition and perform estimation using smoothing techniques combined with a block relaxation algorithm. Unlike previous two-stage approaches, our methodology simultaneously considers tensor decomposition and model estimation, ensuring that the decomposition is optimally-predictive of the response.

主讲人的工作为标量响应变量发展了一个正则化张量分位数回归框架，实现了张量变量数据的鲁棒分析。除了用于识别与阿尔茨海默病有关的海马体区域的神经成像应用之外，张量变量数据在医学、生态学等领域无处不在。区别于之前的张量回归框架，主讲人研究了其张量分位数模型特有的理论，包括建立张量效应估计的重要统计性质和提出估计算法的收敛性质。为了解决张量分位数模型的高维度和分位数损失函数的不可微性，主讲人假设张量效应允许Tucker分解，并使用平滑技术和块松弛相结合的算法进行估计。与以前的两阶段方法不同，主讲人的方法同时考虑张量分解和模型估计，实现了响应变量的最佳预测。