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A disagreement-based active matrix completion approach with provable guarantee

Active matrix completion (AMC) is an effective approach to improve the performance of matrix completion. It actively acquires certain missing entries of a target matrix, with the aim of quickly improving the completion accuracy of the rest. Although this topic is attracting an increasing attention, all existing solutions are heuristic. In this paper, we propose a new active matrix completion approach called Factor-Disagreed AMC (FDAMC), with provably performance guarantee. It is an extension of the popular disagreement-based active statistical learning to the matrix completion task, at both methodological and theoretical levels. Specifically, FDAMC learns two factorization models to complete the matrix, and acquires those missing entries disagreed by the two models in the completion. By employing and modifying the PAC theory, we prove the sample complexity of this approach. A FDAMC algorithm is also presented, with some heuristics included. Finally, we present proof-of-concept experiments and demonstrate the effectiveness of FDAMC on both synthetic and real-world data sets.