Model Selection Under Covariate Shift

Abstract

A common assumption in supervised learning is that the training and test input points follow the same probability distribution. However, this assumption is not fulfilled, e.g., in interpolation, extrapolation, or active learning scenarios. The violation of this assumption—known as the covariate shift—causes a heavy bias in standard generalization error estimation schemes such as cross-validation and thus they result in poor model selection. In this paper, we therefore propose an alternative estimator of the generalization error. Under covariate shift, the proposed generalization error estimator is unbiased if the learning target function is included in the model at hand and it is asymptotically unbiased in general. Experimental results show that model selection with the proposed generalization error estimator is compared favorably to cross-validation in extrapolation.

The authors would like to thank Dr. Motoaki Kawanabe and Dr. Gilles Blanchard for their valuable comments. We acknowledge the Alexander von Humboldt Foundation and from the PASCAL Network of Excellence (EU #506778) for financial support.

An erratum to this chapter can be found at http://dx.doi.org/10.1007/11550907_163 .