Overcoming Representation Bias in Fairness-Aware data Repair using Optimal Transport

Optimal transport (OT) has an important role in transforming data distributions in a manner which engenders fairness. Typically, the OT operators are learnt from the unfair attribute-labelled data, and then used for their repair. Two significant limitations of this approach are as follows: (i) the OT operators for underrepresented subgroups are poorly learnt (i.e. they are susceptible to representation bias); and (ii) these OT repairs cannot be effected on identically distributed but out-of-sample (i.e.\ archival) data. In this paper, we address both of these problems by adopting a Bayesian nonparametric stopping rule for learning each attribute-labelled component of the data distribution. The induced OT-optimal quantization operators can then be used to repair the archival data. We formulate a novel definition of the fair distributional target, along with quantifiers that allow us to trade fairness against damage in the transformed data. These are used to reveal excellent performance of our representation-bias-tolerant scheme in simulated and benchmark data sets.