Subspace learning for high dimensional tensor data

题目：Subspace learning for high dimensional tensor data

报告人：韩岳峰(美国圣母大学）

时间：2023年6月16日（周五）16:00 

地点：海纳苑2幢312

摘要：Motivated by modern scientific research, analysis of tensors (multi-dimensional arrays) has emerged as one of the most important and active areas in modern statistics and data science. High-dimensional tensor data routinely arise in a wide range of applications, such as economics, genetics, microbiome studies, brain imaging, and hyperspectral imaging, due to modern data collection capabilities. In many of these settings, the observed tensors are of high dimension and high order, but the important information may lie in dimension-reduced subspaces induced by various structural conditions. This talk aims to develop new methodologies and theories from a perspective of subspace learning. The talk is divided into three parts. In the first part, we introduce a factor approach for analyzing high dimensional tensor observations, in a form similar to CP tensor decomposition.  We develop a new computationally efficient estimation procedure, which includes a warm-start initialization and an iterative concurrent orthogonalization scheme. We show that the iterative algorithm achieves $\epsilon$-accuracy guarantee within $\log\log(1/\epsilon)$ number of iterations. In the second part, we investigate a tensor factor model with a Tucker type low-rank tensor structure. We propose a novel estimation method that is based on the tensor unfolding of lagged cross-product and iterative orthogonal projections of the original dynamic tensors. We also establish computational and statistical guarantees of the proposed method. In the last part, we illustrate tensor factor models using New York city taxi traffic data

报告人简介：韩岳峰，美国圣母大学（University of Notre Dame）应用计算数学和统计系助理教授。2012年本科毕业于星空体育官方网站统计学专业。2014年在芝加哥大学（University of Chicago）统计系获硕士学位，2019年在芝加哥大学统计系获博士学位，2019-2022在罗格斯大学（Rutgers University）从事博士后研究，2022年入职圣母大学。韩岳峰博士的研究领域广泛，包括张量数据分析、高维统计、时间序列分析、聚类和分类、稳健统计、变点检测、非参数和半参数统计等等。韩岳峰博士在统计学、计量经济学以及机器学习领域的国际顶级期刊（例如：Annals of Statistics，JASA，JBES，Bernoulli, IEEE Transactions on Information Theory等）发表学术论文多篇。

联系人：庞天晓（txpang@zju.edu.cn）