Learning Without Missing-At-Random Prior Propensity-A Generative Approach for Recommender Systems

In recommender systems, it is frequently presumed that missing ratings adhere to a missing at random (MAR) mechanism, implying the absence of ratings is independent of their potential values. However, this assumption fails to hold in real-world scenarios, where users are inclined to rate items they either strongly favor or disfavor, introducing a missing not at random (MNAR) scenario. To tackle this issue, prior researchers have utilized explicit MAR feedbacks to infer the propensities of unobserved, implicit MNAR feedbacks. Nonetheless, acquiring explicit MAR feedbacks is resource-intensive and time-consuming and may not reflect users’ true preferences. Furthermore, most methods have only been tested on synthetic or small-scale datasets, thus their applicability and effectiveness in real-world settings without MAR feedbacks remain unclear. Along these lines, we aim to predict MNAR ratings without MAR prior propensities by exploring the consistency between MAR and MNAR feedbacks and narrowing the gap between them. From the empirical study and preliminary experiment, we hypothesize that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">user preferences</i> can be treated as the common prior propensity for both MAR and MNAR generative processes. In this way, we extend this hypothesis to a more general MNAR scenario: user preferences learned from MNAR can partially substitute for the prior propensities derived from MAR feedbacks for MNAR recommendation tasks. To validate our hypothesis and approach, we develop a lightweight iterative probabilistic matrix factorization framework (lightIPMF) as a practical method of our methodology, utilizing user preferences extracted from MNAR, not MAR, to estimate MNAR feedbacks. Finally, the experimental results show that modeling user preferences can effectively improve MNAR feedback estimation without MAR feedback, and our proposed lightIPMF outperforms the state-of-the-art MNAR methods in predicting MNAR feedbacks.