Aurore Archimbaud, Andreas Alfons, Ines Wilms
Recommender systems are essential tools in the digital landscape for connecting users with content that more closely aligns with their preferences. Matrix completion is a widely used statistical framework for such systems, aiming to predict a user's preferences for items they have not yet rated by leveraging the observed ratings in a partially filled user-item rating matrix. Realistic applications of matrix completion in recommender systems must address several challenges that are too often neglected: (i) the discrete nature of rating-scale data, (ii) the presence of malicious users who manipulate the system to their advantage through the creation of fake profiles, and (iii) missing-not-at-random patterns, where users are more likely to rate items they expect to enjoy. Our goal in this paper is twofold. First, we propose a novel matrix completion method, robust discrete matrix completion (RDMC), designed specifically to handle the discrete nature of sparse rating-scale data and to remain reliable in the presence of adversarial manipulation. We evaluate RDMC through carefully designed experiments and realistic case studies. Our work therefore, secondly, offers a statistically-sound blueprint for future studies on how to evaluate matrix completion methods for recommender systems under realistic scenarios.