  The need to predict or fill-in missing data, often referred to as matrix
completion, is a common challenge in today's data-driven world. Previous
strategies typically assume that no structural difference between observed and
missing entries exists. Unfortunately, this assumption is woefully unrealistic
in many applications. For example, in the classic Netflix challenge, in which
one hopes to predict user-movie ratings for unseen films, the fact that the
viewer has not watched a given movie may indicate a lack of interest in that
movie, thus suggesting a lower rating than otherwise expected. We propose
adjusting the standard nuclear norm minimization strategy for matrix completion
to account for such structural differences between observed and unobserved
entries by regularizing the values of the unobserved entries. We show that the
proposed method outperforms nuclear norm minimization in certain settings.
