  When the performance of a machine learning model varies over groups defined
by sensitive attributes (e.g., gender or ethnicity), the performance disparity
can be expressed in terms of the probability distributions of the input and
output variables over each group. In this paper, we exploit this fact to reduce
the disparate impact of a fixed classification model over a population of
interest. Given a black-box classifier, we aim to eliminate the performance gap
by perturbing the distribution of input variables for the disadvantaged group.
We refer to the perturbed distribution as a counterfactual distribution, and
characterize its properties for common fairness criteria. We introduce a
descent algorithm to learn a counterfactual distribution from data. We then
discuss how the estimated distribution can be used to build a data preprocessor
that can reduce disparate impact without training a new model. We validate our
approach through experiments on real-world datasets, showing that it can repair
different forms of disparity without a significant drop in accuracy.
