Title: Inference and Uncertainty Quantification for Low-Rank Models
Many high-dimensional problems involve reconstruction of a low-rank matrix from incomplete and corrupted 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 examples of low-rank models: (1) noisy matrix completion, and (2) heteroskedastic 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.
The first part of my talk is based on joint work with Cong Ma, Yuling Yan and Jianqing Fan, while the second part is based on joint work with Yuling Yan and Jianqing Fan.
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Meeting ID: 815 7970 4788