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High-dimensional Tensor Learning: Methodology, Theory, and Applications (高维张量学习:方法、理论、应用)

2021-12-23 10:00-11:00 Zoom Meeting(88336789988)

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:

Anru Zhang is the Eugene Anson Stead, Jr. M.D. Associate Professor in the Department of Biostatistics & Bioinformatics, Computer Science, and Mathematics at Duke University. He was an assistant professor of statistics at the University of Wisconsin-Madison in 2015-2021. 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, statistical tensor analysis, computational complexity, and applications in genomics, microbiome, electronic health records, and computational imaging. He received the ASA Gottfried E. Noether Junior Award (2021), a Bernoulli Society New Researcher Award (2021), an ICSA Outstanding Young Researcher Award (2021), and an NSF CAREER Award (2020).

 

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Meeting ID:883 3678 9988