Matrix Completion With Column Manipulation: Near-Optimal Sample-Robustness-Rank Tradeoffs

Abstract—This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return arbitrarily poor results, if even a single column is corrupted. One direct application comes from robust collaborative filtering. Here, some number of users are so-called manipulators who try to skew the predictions of the algorithm by calibrating their inputs to the system. In this paper, we develop an efficient algorithm for this problem based on a combination of a trimming procedure and a convex program that minimizes the nuclear norm and the 1,2 norm. Our theoretical results show that given a vanishing fraction of observed entries, it is nevertheless possible to complete the underlying matrix even when the number of corrupted columns grows. Significantly, our results hold without any assumptions on the locations or values of the ob...

• Type: Journal
• Year: 2016
• Where: TIT
• Authors: Yudong Chen, Huan Xu, Constantine Caramanis, Sujay Sanghavi
• Keywords: Education, TIT 2016