Generalization of Standard Matrix Completion

Joydeep Ghosh and student Suriya Gunasekar work on the generalization of standard matrix completion in various aspects. In previous work, we have proposed tractable estimators for matrix completion with observations arising from heterogeneous datatypes and heterogeneous noise models. In a more recent work, we focus on consistency results for the collective matrix completion problem of jointly recovering a collection of matrices with shared structure. We identify sufficient conditions for consistent estimation of collective matrices and provide the first non–trivial theoretical guarantees for consistency of collective matrix completion using a tractable convex estimator. In another work, we provide unified statistical analysis of matrix completion under general low dimensional structures beyond low--rankness.