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In this article we propose CPrefMiner, a mining technique for learning a Bayesian Preference Network (BPN) from a given sample of user choices. In our approach, user preferences are not static and may vary according to a multitude of user contexts. So, we name them Contextual Preferences. Contextual Preferences can be naturally expressed by a BPN. The method has been evaluated in a series of experiments executed on synthetic and real-world datasets and proved to be efficient to discover user contextual preferences.