The most difficult learning scenario is when the training and test distributions differ both in the data density and in the conditional class distributions. Learning is still possible assuming that some of the learning samples are known to come from the same distribution as the test samples. We formulate a simple nonparametric learner for this task, and apply it for building a "personalized recommender system" that uses the recommendations of other users as possibly useful parts of the training data.

S. Kaski and J. Peltonen belong to the Adaptive Informatics Research Centre, a national centre of excellence of the Academy of Finland. They were supported by grant 108515, and by University of Helsinki's Research Funds. This work was also supported in part by the IST Programme of the European Community, under the PASCAL Network of Excellence, IST-2002-506778. This publication only reflects the authors' views. All rights are reserved because of other commitments.