Filling in Missing Data: Matrix Completion

In practice, missing data is a rampant issue, particularly in frontier spaces where data collection and quality has not yet been standardized. The simplest way to remedy the issue is to fill in missing entries with statistics like mean or median; more intelligent methods include expectation-maximization and multiple imputations, though these methods are not quite scalable. The compressed-sensing literature offers a solution to this problem via matrix completion, which guarantees to recover missing data exactly given only a small number of sampled entries. Matrix completion is both scalable and, as recently shown in a recent paper out of Berkeley, is guaranteed to converge to a globally-optimal solution. In this talk, we will review the original matrix completion algorithm, several improvements and variations, and provide applications.