Matrix completion from a computational statistics perspective

In the matrix completion problem, we seek to estimate the missing entries of a matrix from a small sample of the total number of entries in a matrix. While this task is hopeless in general, structured matrices that are appropriately sampled can be completed with surprising accuracy. In this review, we examine the success behind low-rank matrix completion, one of the most studied and employed versions of matrix completion. Formulating the matrix completion problem as a low-rank matrix estimation problem admits several strengths: good empirical performance on real data, statistical guarantees, and practical algorithms with convergence guarantees. We also examine how matrix completion relates to the classical study of missing data analysis (MDA) in statistics. By drawing on the MDA perspective, we see opportunities to weaken the commonly enforced assumption of missing completely at random in matrix completion. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis.