Pairwise learning underpins implicit collaborative filtering, yet its effectiveness is often hindered by sparse supervision, noisy interactions, and popularity-driven exposure bias. In this paper, we propose Variational Bayesian Personalized Ranking (VarBPR), a tractable variational framework for implicit-feedback pairwise learning that offers principled exposure controllability and theoretical interpretability. VarBPR reformulates pairwise learning as variational inference over discrete latent indexing variables, explicitly modeling noise and indexing uncertainty, and divides training into two stages: variational inference, which solve variational posteriors, and variational learning, which updates model parameters based on these posteriors. In the variational inference stage, we develop a variational formulation that integrates preference alignment, denoising, and popularity debiasing under a unified ELBO/regularization objective, deriving closed-form posteriors with clear control semantics: the prior encodes a target exposure pattern, while temperature/regularization strength controls posterior-prior adherence. As a result, exposure controllability becomes an endogenous and interpretable outcome of variational inference. In the variational learning stage, we propose a posterior-compression objective that reduces the ideal ELBO's computational complexity from polynomial to linear, with the approximation justified by an explicit Jensen-gap upper bound. Theoretically, we provide interpretable generalization guarantees by identifying a structural error component and revealing the opportunity cost of prioritizing certain exposure patterns (e.g., long-tail), offering a concrete analytical lens for designing controllable recommender systems. Empirically, We validate VarBPR across popular backbones; it demonstrates consistent gains in ranking accuracy, enables controlled long-tail exposure, and preserves the linear-time complexity of BPR.

Learning representations from pairwise comparisons has achieved significant success in various fields, including computer vision and information retrieval. In recommendation systems, collaborative filtering algorithms based on pairwise learning are also rooted in this approach. However, a major challenge in collaborative filtering is the lack of labels for negative instances in implicit feedback data, leading to the inclusion of false negatives among randomly selected instances. This issue causes biased optimization objectives and results in biased parameter estimation. In this paper, we propose a novel method to address learning biases arising from implicit feedback data and introduce a modified loss function for pairwise learning, called debiased pairwise loss (DPL). The core idea of DPL is to correct the biased probability estimates caused by false negatives, thereby adjusting the gradients to more closely approximate those of fully supervised data. Implementing DPL requires only a small modification to the existing codebase. Experimental studies on public datasets demonstrate the effectiveness of the proposed method.

How to sample high quality negative instances from unlabeled data, i.e., negative sampling, is important for training implicit collaborative filtering and contrastive learning models. Although previous studies have proposed some approaches to sample informative instances, discriminating false negative from true negative for unbiased negative sampling remains an unsolved problem. On the basis of our order relation analysis of negatives’ scores, we first derive the class conditional density of true negatives and that of false negatives. We next design a Bayesian classifier for negative classification, from which we define a model-agnostic posterior probability estimate of an instance being true negative as a quantitative negative signal measure. We also propose a Bayesian optimal sampling rule to sample high-quality negatives. The proposed Bayesian Negative Sampling (BNS) algorithm has a linear time complexity. Experimental studies validate the superiority of BNS over the peers in terms of better sampling quality and better recommendation performance.1