  Two typical forms of bias in user interaction data with recommender systems
(RSs) are popularity bias and positivity bias, which manifest themselves as the
over-representation of interactions with popular items or items that users
prefer, respectively. Debiasing methods aim to mitigate the effect of selection
bias on the evaluation and optimization of RSs. However, existing debiasing
methods only consider single-factor forms of bias, e.g., only the item
(popularity) or only the rating value (positivity). This is in stark contrast
with the real world where user selections are generally affected by multiple
factors at once. In this work, we consider multifactorial selection bias in
RSs. Our focus is on selection bias affected by both item and rating value
factors, which is a generalization and combination of popularity and positivity
bias. While the concept of multifactorial bias is intuitive, it brings a severe
practical challenge as it requires substantially more data for accurate bias
estimation. As a solution, we propose smoothing and alternating gradient
descent techniques to reduce variance and improve the robustness of its
optimization. Our experimental results reveal that, with our proposed
techniques, multifactorial bias corrections are more effective and robust than
single-factor counterparts on real-world and synthetic datasets.
