A Kernel Two-Sample Test with Selection Bias

Abstract

Hypothesis testing can help decision-making by quantifying distributional differences between two populations from observational data. However, these tests may inherit biases embedded in the data collection mechanism (some instances often being systematically more likely included in our sample) and consistently reproduce biased decisions. We propose a two-sample test that adjusts for selection bias by accounting for differences in marginal distributions of confounding variables. Our test statistic is a weighted distance between samples embedded in a reproducing kernel Hilbert space, whose balancing weights provably correct for bias. We establish the asymptotic distributions under null and alternative hypotheses, and prove the consistency of empirical approximations to the underlying population quantity. We conclude with performance evaluations on artificial data and experiments on treatment effect studies from economics.