Recommendation systems are often evaluated based on users interactions that were collected from an existing, already deployed recommendation system. In this situation, users only provide feedback on the exposed items and they may not leave feedback on other items since they have not been exposed to them by the deployed system. As a result, the collected feedback dataset that is used to evaluate a new model is influenced by the deployed system, as a form of closed loop feedback. In this paper, we show that the typical offline evaluation of recommender systems suffers from the so-called Simpsons paradox. Simpsons paradox is the name given to a phenomenon observed when a significant trend appears in several different sub-populations of observational data but disappears or is even reversed when these sub-populations are combined together. Our in-depth experiments based on stratified sampling reveal that a very small minority of items that are frequently exposed by the deployed system plays a confounding factor in the offline evaluation of recommendation systems. In addition, we propose a novel evaluation methodology that takes into account the confounder, i.e the deployed systems characteristics. Using the relative comparison of many recommendation models as in the typical offline evaluation of recommender systems, and based on the Kendall rank correlation coefficient, we show that our proposed evaluation methodology exhibits statistically significant improvements of 14% and 40% on the examined open loop datasets (Yahoo! and Coat), respectively, in reflecting the true ranking of systems with an open loop (randomised) evaluation in comparison to the standard evaluation.
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