Tripartite Collaborative Filtering with Observability and Selection for Debiasing Rating Estimation on Missing-Not-at-Random Data

Most collaborative filtering (CF) models estimate missing ratings with an implicit assumption that the ratings are missing-at-random, which may cause the biased rating estimation and degraded performance since recent deep exploration shows that ratings may likely be missing-not-at-random (MNAR). To debias MNAR rating estimation, we introduce item observability and user selection to depict the generation of MNAR ratings and propose a tripartite CF (TCF) framework to jointly model the triple aspects of rating generation: item observability, user selection, and ratings, and to estimate the MNAR ratings. An item observability variable is introduced to a complete observability model to infer whether an item is observable to a user. TCF also conducts a complete rating model for rating generation and utilizes a user selection model dependent on the item observability and rating values to model user selection of the observable items. We further elaborately instantiate TCF as a Tripartite Probabilistic Matrix Factorization model (TPMF) by leveraging the probabilistic matrix factorization. Besides, TPMF introduces multifaceted dependency between user selection and ratings to model the influence of user selection on ratings. Extensive experiments on synthetic and real-world datasets show that modeling item observability and user selection effectively debias MNAR rating estimation, and TPMF outperforms the state-of-the-art methods in estimating the MNAR ratings.