Can we learn about object classes in images by looking at a collection of relevant 3D models? Or if we want to learn about human (inter-)actions in images, can we benefit from videos or abstract illustrations that show these actions? A common aspect of these settings is the availability of additional or privileged data that can be exploited at training time and that will not be available and not of interest at test time. We seek to generalize the learning with privileged information (LUPI) framework, which requires additional information to be defined per image, to the setting where additional information is a data collection about the task of interest. Our framework minimizes the distribution mismatch between errors made in images and in privileged data. The proposed method is tested on four publicly available datasets: Image+ClipArt, Image+3Dobject, and Image+ Video. Experimental results reveal that our new LUPI paradigm naturally addresses the cross-dataset learning.