HoORaYs: High-order optimization of rating distance for recommender systems

Latent factor models have become a prevalent method in recom-mender systems, to predict users' preference on items based on the historical user feedback. Most of the existing methods, explicitly or implicitly, are built upon the first-order rating distance principle, which aims to minimize the difference between the estimated and real ratings. In this paper, we generalize such first-order rating distance principle and propose a new latent factor model (HOORAYS) FOR recommender systems. The core idea of the proposed method is to explore high-order rating distance, which aims to minimize not only (i) the difference between the estimated and real ratings of the same (user, item) pair (i.e., the first-order rating distance), but also (ii) the difference between the estimated and real rating difference of the same user across different items (i.e., the second-order rating distance). We formulate it as a regularized optimization problem, and propose an effective and scalable algorithm to solve it. Our analysis from the geometry and Bayesian perspectives indicate that by exploring the high-order rating distance, it helps to reduce the variance of the estimator, which in turns leads to better generalization performance (e.g., smaller prediction error). We evaluate the proposed method on four real-world data sets, two with explicit user feedback and the other two with implicit user feedback. Experimental results show that the proposed method consistently outperforms the state-of-the-art methods in terms of the prediction accuracy.