Discriminative Learning Under Covariate Shift

Steffen Bickel, Michael Brückner, Tobias Scheffer.

Year: 2009, Volume: 10, Issue: 75, Pages: 2137−2155


We address classification problems for which the training instances are governed by an input 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. The problem of learning under covariate shift can be written as an integrated optimization problem. Instantiating the general optimization problem leads to a kernel logistic regression and an exponential model classifier for covariate shift. The optimization problem is convex under certain conditions; our findings also clarify the relationship to the known kernel mean matching procedure. We report on experiments on problems of spam filtering, text classification, and landmine detection.