Mixture Matrix Completion
Abstract
Completing a data matrix X has become an ubiquitous problem in modern data science, with applications in recommender systems, computer vision, and networks inference, to name a few. One typical assumption is that X is lowrank. A more general model assumes that each column of X corresponds to one of several lowrank matrices. This paper generalizes these models to what we call mixture matrix completion (MMC): the case where each entry of X corresponds to one of several lowrank matrices. MMC is a more accurate model for recommender systems, and brings more flexibility to other completion and clustering problems. We make four fundamental contributions about this new model. First, we show that MMC is theoretically possible (wellposed). Second, we give its precise informationtheoretic identifiability conditions. Third, we derive the sample complexity of MMC. Finally, we give a practical algorithm for MMC with performance comparable to the stateoftheart for simpler related problems, both on synthetic and real data.
 Publication:

arXiv eprints
 Pub Date:
 August 2018
 arXiv:
 arXiv:1808.00616
 Bibcode:
 2018arXiv180800616P
 Keywords:

 Computer Science  Machine Learning;
 Statistics  Machine Learning