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Recent years have seen a surge of machine learning approaches aimed atreducing disparities in model outputs across different subgroups. In manysettings, training data may be used in multiple downstream applications bydifferent users, which means it may be most effective to intervene on thetraining data itself. In this work, we present FairWASP, a novel pre-processingapproach designed to reduce disparities in classification datasets withoutmodifying the original data. FairWASP returns sample-level weights such thatthe reweighted dataset minimizes the Wasserstein distance to the originaldataset while satisfying (an empirical version of) demographic parity, apopular fairness criterion. We show theoretically that integer weights areoptimal, which means our method can be equivalently understood as duplicatingor eliminating samples. FairWASP can therefore be used to construct datasetswhich can be fed into any classification method, not just methods which acceptsample weights. Our work is based on reformulating the pre-processing task as alarge-scale mixed-integer program (MIP), for which we propose a highlyefficient algorithm based on the cutting plane method. Experiments on syntheticdatasets demonstrate that our proposed optimization algorithm significantlyoutperforms state-of-the-art commercial solvers in solving both the MIP and itslinear program relaxation. Further experiments highlight the competitiveperformance of FairWASP in reducing disparities while preserving accuracy indownstream classification settings.

FairWASP: Fast and Optimal Fair Wasserstein Pre-processing