Discriminative learning for differing training and test distributions

We address classification problems for which the training instances are governed by a distribution that is allowed to differ arbitrarily from the test distribution---problems also referred to as classification under covariate shift. We derive a solution that is purely discriminative: neither training nor test distribution are modeled explicitly. We formulate the general problem of learning under covariate shift as an integrated optimization problem. We derive a kernel logistic regression classifier for differing training and test distributions.