Double-Weighting for Covariate Shift Adaptation
This addresses covariate shift adaptation for machine learning practitioners, offering an incremental improvement over existing weighting methods.
The paper tackles covariate shift adaptation in supervised learning by proposing a minimax risk classification approach that weights both training and testing samples, avoiding limitations of existing methods like poor performance under support mismatch or large ratio values. It achieves enhanced classification performance in experiments and shows a significant increase in effective sample size compared to reweighted methods.
Supervised learning is often affected by a covariate shift in which the marginal distributions of instances (covariates $x$) of training and testing samples $\mathrm{p}_\text{tr}(x)$ and $\mathrm{p}_\text{te}(x)$ are different but the label conditionals coincide. Existing approaches address such covariate shift by either using the ratio $\mathrm{p}_\text{te}(x)/\mathrm{p}_\text{tr}(x)$ to weight training samples (reweighted methods) or using the ratio $\mathrm{p}_\text{tr}(x)/\mathrm{p}_\text{te}(x)$ to weight testing samples (robust methods). However, the performance of such approaches can be poor under support mismatch or when the above ratios take large values. We propose a minimax risk classification (MRC) approach for covariate shift adaptation that avoids such limitations by weighting both training and testing samples. In addition, we develop effective techniques that obtain both sets of weights and generalize the conventional kernel mean matching method. We provide novel generalization bounds for our method that show a significant increase in the effective sample size compared with reweighted methods. The proposed method also achieves enhanced classification performance in both synthetic and empirical experiments.