  Covariate shift in the test data is a common practical phenomena that can
significantly downgrade both the accuracy and the fairness performance of the
model. Ensuring fairness across different sensitive groups under covariate
shift is of paramount importance due to societal implications like criminal
justice. We operate in the unsupervised regime where only a small set of
unlabeled test samples along with a labeled training set is available. Towards
improving fairness under this highly challenging yet realistic scenario, we
make three contributions. First is a novel composite weighted entropy based
objective for prediction accuracy which is optimized along with a
representation matching loss for fairness. We experimentally verify that
optimizing with our loss formulation outperforms a number of state-of-the-art
baselines in the pareto sense with respect to the fairness-accuracy tradeoff on
several standard datasets. Our second contribution is a new setting we term
Asymmetric Covariate Shift that, to the best of our knowledge, has not been
studied before. Asymmetric covariate shift occurs when distribution of
covariates of one group shifts significantly compared to the other groups and
this happens when a dominant group is over-represented. While this setting is
extremely challenging for current baselines, We show that our proposed method
significantly outperforms them. Our third contribution is theoretical, where we
show that our weighted entropy term along with prediction loss on the training
set approximates test loss under covariate shift. Empirically and through
formal sample complexity bounds, we show that this approximation to the unseen
test loss does not depend on importance sampling variance which affects many
other baselines.
