報告題目: Matrix Completion with Covariate Information

　　報告人: 陳松蹊 教授 北京大學(xué)

　  報告時間: 2019.07.11(周四)下午16:00--17:00

　　報告地點: 新大樓1217報告廳

　　摘要: This paper investigates the problem of matrix completion from corrupted data, when additional covariates are available. Despite being seldomly considered in the matrix completion literature, these covariates often provide valuable information for completing the unobserved entries of the high-dimensional target matrix A0. Given a covariate matrix X with its rows representing the row covariates of A0, we consider a column-space-decomposition model A0 = X beta0+B0 where beta0 is a coefficient matrix and B0 is a low-rank matrix orthogonal to X in terms of column space. This model facilitates a clear separation between the interpretable covariate effects (X beta0) and the flexible hidden factor effects (B0). Besides, our work allows the probabilities of observation to depend on the covariate matrix, and hence a missing-at-random mechanism is permitted. We propose a novel penalized estimator for A0 by utilizing both Frobenius-norm and nuclear-norm regularizations with an efficient and scalable algorithm. Asymptotic convergence rates of the proposed estimators are studied. The empirical performance of the proposed methodology is illustrated via both numerical experiments and a real data application.

　　報告人介紹: 陳松蹊，國家特聘專家，北京大學(xué)講席教授，北京大學(xué)統(tǒng)計科學(xué)中心聯(lián)席主任。他是美國科學(xué)促進(jìn)會會員，數(shù)理統(tǒng)計學(xué)會資深會員，美國統(tǒng)計學(xué)會會員，國際統(tǒng)計學(xué)會當(dāng)選會員，國際數(shù)理統(tǒng)計學(xué)會(IMS) 理事會常務(wù)理事。同時擔(dān)任The Annals of Statistics編委（2010-2019年），美國統(tǒng)計學(xué)會會刊編委（自2018年），Environmentrics編委（自2018年）。自2015年他的團(tuán)隊在評估中國北方地區(qū)大氣污染的變化，提出了去除氣象干擾的方法，已經(jīng)發(fā)布六份空氣質(zhì)量報告。目前主持國家重點研發(fā)專項項目“空氣質(zhì)量統(tǒng)計診斷模型”，兩項自科基金重點項目。