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Covariate shift in the test data is a common practical phenomena that cansignificantly downgrade both the accuracy and the fairness performance of themodel. Ensuring fairness across different sensitive groups under covariateshift is of paramount importance due to societal implications like criminaljustice. We operate in the unsupervised regime where only a small set ofunlabeled test samples along with a labeled training set is available. Towardsimproving fairness under this highly challenging yet realistic scenario, wemake three contributions. First is a novel composite weighted entropy basedobjective for prediction accuracy which is optimized along with arepresentation matching loss for fairness. We experimentally verify thatoptimizing with our loss formulation outperforms a number of state-of-the-artbaselines in the pareto sense with respect to the fairness-accuracy tradeoff onseveral standard datasets. Our second contribution is a new setting we termAsymmetric Covariate Shift that, to the best of our knowledge, has not beenstudied before. Asymmetric covariate shift occurs when distribution ofcovariates of one group shifts significantly compared to the other groups andthis happens when a dominant group is over-represented. While this setting isextremely challenging for current baselines, We show that our proposed methodsignificantly outperforms them. Our third contribution is theoretical, where weshow that our weighted entropy term along with prediction loss on the trainingset approximates test loss under covariate shift. Empirically and throughformal sample complexity bounds, we show that this approximation to the unseentest loss does not depend on importance sampling variance which affects manyother baselines.

Fairness under Covariate Shift: Improving Fairness-Accuracy tradeoff with few Unlabeled Test Samples