BPR: Bayesian Personalized Ranking from Implicit Feedback

TL;DR

This paper tackles personalized ranking from implicit feedback by deriving a Bayesian posterior objective (BPR-Opt) that directly optimizes pairwise item preferences for each user. It introduces LearnBPR, a bootstrap-SGD algorithm, and demonstrates how to apply it to matrix factorization and adaptive kNN models, yielding superior AUC-based ranking performance over traditional MF and kNN learning methods. The work also situates BPR within the broader landscape of WR-MF and MMMF, showing that pairwise, probabilistic ranking optimization better captures the goal of recommendation than item-score regression. The proposed approach offers a scalable, principled framework for optimizing rankings in implicit-feedback settings with strong practical impact for recommender systems.

Abstract

Item recommendation is the task of predicting a personalized ranking on a set of items (e.g. websites, movies, products). In this paper, we investigate the most common scenario with implicit feedback (e.g. clicks, purchases). There are many methods for item recommendation from implicit feedback like matrix factorization (MF) or adaptive knearest-neighbor (kNN). Even though these methods are designed for the item prediction task of personalized ranking, none of them is directly optimized for ranking. In this paper we present a generic optimization criterion BPR-Opt for personalized ranking that is the maximum posterior estimator derived from a Bayesian analysis of the problem. We also provide a generic learning algorithm for optimizing models with respect to BPR-Opt. The learning method is based on stochastic gradient descent with bootstrap sampling. We show how to apply our method to two state-of-the-art recommender models: matrix factorization and adaptive kNN. Our experiments indicate that for the task of personalized ranking our optimization method outperforms the standard learning techniques for MF and kNN. The results show the importance of optimizing models for the right criterion.

Figures (6)

• Figure 1: On the left side, the observed data$S$ is shown. Learning directly from $S$ is not feasible as only positive feedback is observed. Usually negative data is generated by filling the matrix with 0 values.
• Figure 2: On the left side, the observed data$S$ is shown. Our approach creates user specific pairwise preferences $i>_{u} j$ between a pair of items. On the right side, plus ( + ) indicates that a user prefers item $i$ over item $j$; minus (-) indicates that he prefers $j$ over $i$.
• Figure 3: Loss functions for optimizing the AUC. The non-differentiable Heaviside$H(x)$ is often approximated by the sigmoid $\sigma(x)$. Our MLE derivation suggests to use $\ln \sigma(x)$ instead.
• Figure 4: Convergence on Rossmann dataset
• Figure 5: Area under the ROC curve (AUC) prediction quality for the Rossmann dataset and a Netflix subsample. Our BPR optimizations for matrix factorization BPR-MF and k-nearest neighbor BPR-kNN are compared against weighted regularized matrix factorization (WR-MF) [5, 10], singular value decomposition (SVD-MF), k-nearest neighbor (Cosine-kNN) [2] and the most-popular model. For the factorization methods BPR-MF, WR-MF and SVD-MF, the model dimensions are increased from 8 to 128 dimensions. Finally,$n p_{\max }$ is the theoretical upper bound for any non-personalized ranking method.