SPEAKER: Xiaojun Mao
Matrix Completion under Low-Rank Missing Mechanism
This paper investigates the problem of matrix completion from corrupted data when a low-rank missing mechanism is considered. The better recovery of missing mechanism often helps to complete the unobserved entries of the high-dimensional target matrix A0. We consider a low-rank matrix M0 as the hidden linear predictor and generate the probabilities of observation Theta0 through some general inverse link functions f. We estimate M0 through an additive model and modify the estimator by some truncations. Instead of the uniform objective function, we adopt a weighted version by using the estimated probabilities of observation as the inverse probability weighting. Asymptotic convergence rates of the proposed estimators for missingness M0, Theta0 and target matrix A0 are studied. The empirical performance of the proposed methodology is illustrated via both numerical experiments and one real data application.