Abstract: The analysis of tensor data has become an active research topic in statistics and data science recently. Many high-order datasets arising from a wide range of modern applications, such as genomics, material science, and neuroimaging analysis, requires modeling with high-dimensional tensors. In addition, tensor methods provide unique perspectives and solutions to many high-dimensional problems where the observations are not necessarily tensors. High-dimensional tensor problems generally possess distinct characteristics that pose unprecedented challenges to the statistical community. There is a clear need to develop novel methods, algorithms, and theories to analyze the high-dimensional tensor data.
In this talk, we discuss some recent advances in high-dimensional tensor data analysis through several fundamental topics and their applications in microscopy imaging and neuroimaging. We will also illustrate how we develop new statistically optimal methods, computationally efficient algorithms, and fundamental theories that exploit information from high-dimensional tensor data based on the modern theory of computation, non-convex optimization, applied linear algebra, and high-dimensional statistics.
Bio: Anru Zhang has been a tenure-track assistant professor of statistics at the University of Wisconsin-Madison since 2015. Currently, he is holding a visiting professor position at the Department of Biostatistics & Bioinformatics at Duke University. He obtained his Bachelor’s degree in mathematics from Peking University in 2010 and his Ph.D. from the University of Pennsylvania in 2015. His work focuses on high-dimensional statistical inference, non-convex optimization, computational complexity, statistical tensor analysis, statistical learning theory, and applications in genomics, microbiome, computational imaging. He is the recipient of the NSF CAREER Award (2020) and the Dean’s Scholar at the University of Pennsylvania (2015).