Regular Paper Direct Density Ratio Estimation for Large-scale Covariate Shift Adaptation

Covariate shift is a situation in supervised learning where training and test inputs follow different distributions even though the functional relation remains unchanged. A common approach to compensating for the bias caused by covari-ate shift is to reweight the loss function according to the importance, which is the ratio of test and training densities. We propose a novel method that allows us to directly estimate the importance from samples without going through the hard task of density estimation. An advantage of the proposed method is that the computation time is nearly independent of the number of test input samples, which is highly beneficial in recent applications with large numbers of unlabeled samples. We demonstrate through experiments that the proposed method is computationally more efficient than existing approaches with com-parable accuracy. We also describe a promising result for large-scale covariate shift adaptation in a natural language processing task. 1