Event Date
Speaker: Yuling Yan, PhD Candidate, Princeton University
Title: "Inference and Uncertainty Quantification for Low-Rank Models"
Abstract: Many high-dimensional problems involve reconstruction of a low-rank matrix from highly incomplete and noisy observations. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of the obtained low-rank estimates, and how to construct valid yet short confidence intervals for the unknown low-rank matrix.
In this talk, I will discuss how to perform inference and uncertainty quantification for two widely encountered low-rank models: (1) noisy matrix completion, and (2) PCA with missing data. For both problems, we identify statistically efficient estimators that admit non-asymptotic distributional characterizations, which in turn enable optimal construction of confidence intervals for, say, the unseen entries of the low-rank matrix of interest. Our inferential procedures do not rely on sample splitting, thus avoiding unnecessary loss of data efficiency. All this is accomplished by a powerful leave-one-out analysis framework that originated from probability and random matrix theory.
This is based on joint work with Yuxin Chen, Jianqing Fan and Cong Ma.
SEMINAR TIME/DATE: Friday, January 13, 11:00am
LOCATION: MSB 1147