  Most data for evaluating and training recommender systems is subject to
selection biases, either through self-selection by the users or through the
actions of the recommendation system itself. In this paper, we provide a
principled approach to handling selection biases, adapting models and
estimation techniques from causal inference. The approach leads to unbiased
performance estimators despite biased data, and to a matrix factorization
method that provides substantially improved prediction performance on
real-world data. We theoretically and empirically characterize the robustness
of the approach, finding that it is highly practical and scalable.
