  Varying domains and biased datasets can lead to differences between the
training and the target distributions, known as covariate shift. Current
approaches for alleviating this often rely on estimating the ratio of training
and target probability density functions. These techniques require parameter
tuning and can be unstable across different datasets. We present a new method
for handling covariate shift using the empirical cumulative distribution
function estimates of the target distribution by a rigorous generalization of a
recent idea proposed by Vapnik and Izmailov. Further, we show experimentally
that our method is more robust in its predictions, is not reliant on parameter
tuning and shows similar classification performance compared to the current
state-of-the-art techniques on synthetic and real datasets.
