Matrix Completion under Low-Rank Missing Mechanism
This addresses matrix completion for corrupted data by moving beyond uniform missing assumptions, though it is incremental in improving estimation methods.
The authors tackled matrix completion under a low-rank missing mechanism, deriving optimal asymptotic convergence rates for both observation probability and target matrix estimators.
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion methods often assume a simple uniform missing mechanism. In this work, we study matrix completion from corrupted data under a novel low-rank missing mechanism. The probability matrix of observation is estimated via a high dimensional low-rank matrix estimation procedure, and further used to complete the target matrix via inverse probabilities weighting. Due to both high dimensional and extreme (i.e., very small) nature of the true probability matrix, the effect of inverse probability weighting requires careful study. We derive optimal asymptotic convergence rates of the proposed estimators for both the observation probabilities and the target matrix.