Collaborative Preference Learning Alexandros Karatzoglou 1 and Markus Weimer 2 1 INSA de Rouen, LITIS, France, alexis@ci.tuwien.ac.at 2 Technische Universit¨ at Darmstadt, Germany, weimer@acm.org Abstract. Every recommender system needs the notion of preferences of a user in order to suggest one item and not another. However, current recommender algorithms deduct these preferences by first predicting an actual rating of the items and then sorting those. Departing from this, we present an algorithm that is capable of directly learning the preference function from given ratings. The presented approach combines recent results on preference learn- ing, state of the art optimization algorithms and the large margin ap- proach to capacity control. The algorithm follows the matrix factoriza- tion paradigm to collaborative filtering. Maximum Margin Matrix Fac- torization (MMMF) has been introduced to control the capacity of the prediction in order to avoid overfitting. We present an extension to this approach that is capable of using the methodology developed by the Learning to Rank community to learn a ranking of unrated items for each user. In addition, we integrate several recently proposed extensions to MMMF into one coherent framework where they can be combined in a mix-and-match fashion. 1 Introduction Recommender systems are used by many websites to suggest content, products or services to their visitors. However, suggesting the right items is a highly nontrivial task: (1) There are many items to choose from. (2) Customers are willing to consider only a small number of recommendations (typically in the order of ten). Thus, the recommender system needs to have a good grasp on the user’s preferences in order to suggest one item and not another. Recommender algorithms often deduct these preferences by first predicting an actual rating of the items and then sorting those. This does not do justice to the way the resulting rankings are usually used: Users are presented only a limited subset of the items. Or a ranked list is shown where the top k (usually 10) items are presented on the first page and all others are hidden on subsequent pages. The procedure outlined above does not guarantee to do well in these sce- narios, for example because it puts equal emphasis on all predictions as opposed to just the top k. The question of how to evaluate a predicted ranking is nontrivial in itself which results in a plethora of different ranking measures. Recently, the machine learning community developed approaches to optimize the prediction directly