Using Hyperbolic Cross Approximation to measure and compensate Covariate Shift

The concept of covariate shift in supervised data analysis describes a difference between the training and test distribution while the conditional distribution remains the same. To improve the prediction performance one can address such a change by using individual weights for each training datapoint, which emphasizes the training points close to the test data set so that these get a higher significance. We propose a new method for calculating such weights by minimizing a Fourier series approximation of distance measures, in particular we consider the total variation distance, the Euclidean distance and Kullback-Leibler divergence. To be able to use the Fourier approach for higher dimensional data, we employ the so-called hyperbolic cross approximation. Results show that the new approach can compete with the latest methods and that on real life data an improved performance can be obtained.