报告简介  Abstract

 We introduce a flexible framework for making inferences about general linear forms of a large matrix based on noisy observations of a subset of its entries. In particular, under mild regularity conditions, we develop a universal procedure to construct asymptotically normal estimators of its linear forms through double-sample debiasing and low-rank projection whenever an entry-wise consistent estimator of the matrix is available. These estimators allow us to subsequently construct confidence intervals for and test hypotheses about the linear forms. Our proposal was motivated by a careful perturbation analysis of the empirical singular spaces under the noisy matrix completion model which might be of independent interest. The practical merits of our proposed inference procedure are demonstrated on both simulated and real-world data examples.

嘉宾简介  About the Speaker

Dr. Dong XIA is now working as an assistant professor at the Department of Mathematics, HKUST. He obtained his B.S. Degree from USTC in 2011, and Ph.D. Degree from Georgia Tech in 2016. He was a visiting assistant professor (2016-2017) at UW-Madison and post-doctoral scientist (2017-2018) at Columbia University. His research area focuses on high dimensional statistics mainly on the estimation and inference for large matrix or tensorial datasets, with applications in quantum state tomography, network data analysis and recommender systems.

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