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20190605 张安如:Optimal Tensor Singular Value Decomposition
时间:2019-05-24

报告时间:2019年6月5日  14:30-15:30

报告地点:明德主楼1016会议室

报告主题Optimal Tensor Singular Value Decomposition


报告摘要

  High-dimensional high-order data arise in many modern scientific applications including genomics, brain imaging, and social science. In this talk, we consider the methods, theories, and computations for tensor singular value decomposition (tensor SVD), which aims to extract the hidden low-rank structure from high-dimensional high-order data. First, comprehensive results are developed on both the statistical and computational limits for tensor SVD under the general scenario. This problem exhibits three different phases according to signal-noise-ratio (SNR), and the minimax-optimal statistical and/or computational results are developed in each of the regimes. In addition, we further consider the sparse tensor singular value decomposition which allows more robust estimation under sparsity structural assumptions. A novel sparse tensor alternating thresholding algorithm is proposed. Both the optimal theoretical results and numerical analyses are provided to guarantee the performance of the proposed procedure.



报告人简介

  Anru Zhang is an assistant professor at the Department of Statistics, University of Wisconsin-Madison. He is also affiliated to Machine Learning Group and Institute for Foundations of Data Science at UW-Madison. He obtained the PhD degree from University of Pennsylvania in 2015 and the bachelors degree from Peking University in 2010. His current research interests include High-dimensional Statistical Inference, Tensor Data Analysis, and Statistical Learning Theory. He received grants from the National Science Foundation and National Institute of Health.