Matrix Completion with Noisy Side Information ∗ ∗ University of Texas at Austin

We study the matrix completion problem with side information. Side information has been considered in several matrix completion applications, and has been empirically shown to be useful in many cases. Recently, researchers studied the effect of side information for matrix completion from a theoretical viewpoint,showing that sample complexity can be significantly reduced given completely clean features. However, since in reality most given features are noisy or only weakly informative, the development of a model to handle a general feature set, and investigation of how much noisy features can help matrix recovery, remains an important issue. In this paper, we propose a novel model that balances between features and observations simultaneously in order to leverage feature information yet be robust to feature noise. Moreover, we study the effect of general features in theory and show that by using our model, the sample complexity can be lower than matrix completion as long as features are sufficiently informative.