Matrix Completion under Low-Rank Missing Mechanism
This talk 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 completing the unobserved entries of the high-dimensional target matrix. Instead of the widely used uniform risk function, we weight the observations by inverse probabilities of observation, which are estimated through a specifically designed high-dimensional estimation procedure. Asymptotic convergence rates of the proposed estimators for both the observation probabilities and the target matrix are studied. The empirical performance of the proposed methodology is illustrated via both numerical experiments and a real data application.
About the Speaker:
Xiaojun Mao is an assistant professor of the School of Data Science at Fudan University. He received his PhD from Iowa State University in 2018. Dr. Mao's research interests include Matrix Completion, Recommender Systems, Regularization methods (e.g. ℓ1, ℓ2 and nuclear-norm penalty) and Genomic Prediction.