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Explore a comprehensive lecture on inference and uncertainty quantification for noisy matrix completion, part of the TRIAD Distinguished Lecture Series delivered by Yuxin Chen from Princeton University. Delve into the development of a simple procedure to compensate for bias in convex and nonconvex estimators, leading to nearly precise non-asymptotic distributional characterizations. Learn how these findings enable optimal construction of confidence intervals and regions for missing entries and low-rank factors. Discover the advantages of this approach, which avoids sample splitting and unnecessary loss of data efficiency. Gain insights into the sharp characterization of estimation accuracy for de-biased estimators, marking them as the first tractable algorithms to achieve full statistical efficiency. Examine the intimate link between convex and nonconvex optimization that underpins this analysis, presented as joint work with Cong Ma, Yuling Yan, Yuejie Chi, and Jianqing Fan.
