Large-Scale Recommendation Systems

Recommender systems are widely used in the digital landscape to match users with content fitting their preferences. However, growing concerns about fake accounts, strategic manipulation, and other deceptive online behavior place increasing pressure on the reliability of these systems. A common statistical approach behind recommender systems is so-called matrix completion, which predicts how users would rate items they have not yet consumed based on patterns in observed ratings. Realistically applying matrix completion methods requires jointly addressing several overlooked challenges: (i) ratings on discrete scales (such as 1--5 stars); (ii) the presence of malicious users who deliberately manipulate the system to their advantage through fake profiles; (iii) ratings missing not at random since users are more likely to consume items they expect to like; and (iv) fostering transparency, reproducibility, and stability. We jointly address these challenges by proposing a novel method, Robust Discrete Matrix Completion (RDMC), designed to capture the key characteristics of sparse rating data while remaining reliable in the presence of manipulation. We evaluate RDMC through two case studies and carefully designed simulation experiments. Our work thereby offers a statistically-sound blueprint for future studies on how to evaluate recommender systems under realistic scenarios.

Many important tasks of large-scale recommender systems can be naturally cast as testing multiple linear forms for noisy matrix completion. These problems, however, present unique challenges because of the subtle bias-and-variance tradeoff of and an intricate dependence among the estimated entries induced by the low-rank structure. In this paper, we develop a general approach to overcome these difficulties by introducing new statistics for individual tests with sharp asymptotics both marginally and jointly, and utilizing them to control the false discovery rate (FDR) via a data splitting and symmetric aggregation scheme. We show that valid FDR control can be achieved with guaranteed power under nearly optimal sample size requirements using the proposed methodology. Extensive numerical simulations and real data examples are also presented to further illustrate its practical merits.