Recommender systems make use of a database of user ratings to generate personalized recommendations and help people to find relevant products, items, or documents. In this paper, we present a probabilistic, model-based framework for user ratings based on a novel collaborative filtering technique that performs an automatic decomposition of user preferences. Our approach has several benefits, including highly accurate predictions, task-optimized model learning, mining of interest groups and patterns, as well as a highly efficient and scalable computation of predictions and recommendation lists.