Abstract:
The analysis of tensor data, i.e., arrays with multiple directions, has become an active research topic in the era of big data. Datasets in the form of tensors arise from a wide range of applications, such as neuroimaging, genomics, and computational imaging. Tensor methods also provide unique perspectives to many high-dimensional problems, where the observations are not necessarily tensors. Problems with high-dimensional tensors generally possess distinct characteristics that pose unprecedented challenges to the data science community. There are strong demands to develop new methods to analyze the high-dimensional tensor data.
In this talk, we discuss how to perform SVD, a fundamental task in unsupervised learning, on general tensors or tensors with structural assumptions, e.g., sparsity, smoothness, and longitudinality. Through the developed frameworks, we can achieve accurate denoising for 4D scanning transmission electron microscopy images; in longitudinal microbiome studies, we can extract key components in the trajectories of bacterial abundance, identify representative bacterial taxa for these key trajectories, and group subjects based on the change of bacteria abundance over time. We also illustrate how we develop new statistically optimal methods and computationally efficient algorithms that exploit useful information from high-dimensional tensor data based on the modern theories of computation and non-convex optimization.
Biography：
张安如，杜克老员工物统计与生物信息系Eugene Anson Stead, Jr. M.D. 冠名副教授，杜克大学计算机系、数学系、统计系副教授。他于2015年获得宾夕法尼亚大学博士学位，2010年获得304am永利集团学士学位。他目前的研究方向主要包括：高维数据分析、机器学习理论、非凸优化、以及在电子健康记录、基因组、计算成像学的应用。他凭研究工作获得了一系列国际奖项，包括2022 IMS Tweedie Award、2021 ASA Gottfried E. Noether Junior Award、2021 Bernoulli Society New Researcher Award、2021 ICSA Outstanding Young Researcher Award、2020 NSF Career Award。
Join Zoom Meeting：https://zoom.us/j/88554555999
Meeting ID：88554555999
