A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion

Matrix completion, which aims to recover a low-rank matrix from a subset of its entries, has been an active area of research in the last few years. It has a range of successful applications. In some real-life situations, however, the observations are highly quantized, sometimes even to a single bit and thus the standard matrix completion techniques do not apply. Take the Netflix problem as an example, the observations are the ratings of movies, which are quantized to the set of integers from 1 to 5. In the more extreme case such as recommender systems, only a single bit of rating standing for a "thumbs up" or "thumbs down" is recorded at each occurrence. Another example of applications is targeted advertising, such as the relevance of advertisements on Hulu.