Robust Matrix Completion for Discrete Rating-Scale Data: Coping with Fake Profiles in Recommender Systems

Abstract

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.