Scalable Collaborative Ranking for Personalized Prediction
Ben Dai, Xiaotong T. Shen, Junhui Wang, Annie Qu · Journal of the American Statistical Association · 2019
Ben Daiab, Xiaotong Shena, Junhui Wangb & Annie Quc* a School of Statistics, University of Minnesota , Minneapolis , MN ; b School of Data Science, City University of Hong Kong , Kowloon Tong, Hong Kong ; c Department of Statistics, University of Illinois at Urbana Champaign , Champaign , IL Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA. CONTACT Annie Qu [email protected] Department of Statistics, University of Illinois at Urbana Champaign , Champaign , IL 61820.AbstractPersonalized prediction presents an important yet challenging task, which predicts user-specific preferences on a large number of items given limited information. It is often modeled as certain recommender systems focusing on ordinal or continuous ratings, as in collaborative filtering and content-based filtering. In this article, we propose a new collaborative ranking system to predict most-preferred items for each user given search queries. Particularly, we propose a ψ-ranker based on ranking functions incorporating information on users, items, and search queries through latent factor models. Moreover, we show that the proposed nonconvex surrogate pairwise ψ-loss performs well under four popular bipartite ranking losses, such as the sum loss, pairwise zero-one loss, discounted cumulative gain, and mean average precision. We develop a parallel computing strategy to optimize the intractable loss of two levels of nonconvex components through difference of convex programming and block successive upper-bound minimization. Theoretically, we establish a probabilistic error bound for the ψ-ranker and show that its ranking error has a sharp rate of convergence in the general framework of bipartite ranking, even when the dimension of the model parameters diverges with the sample size. Consequently, this result also indicates that the ψ-ranker performs better than two major approaches in bipartite ranking: pairwise ranking and scoring. Finally, we demonstrate the utility of the ψ-ranker by comparing it with some strong competitors in the literature through simulated examples as well as Expedia booking data. Supplementary materials for this article are available online.