  In past work on fairness in machine learning, the focus has been on forcing
the prediction of classifiers to have similar statistical properties for people
of different demographics. To reduce the violation of these properties,
fairness methods usually simply rescale the classifier scores, ignoring
similarities and dissimilarities between members of different groups. Yet, we
hypothesize that such information is relevant in quantifying the unfairness of
a given classifier. To validate this hypothesis, we introduce Optimal Transport
to Fairness (OTF), a method that quantifies the violation of fairness
constraints as the smallest Optimal Transport cost between a probabilistic
classifier and any score function that satisfies these constraints. For a
flexible class of linear fairness constraints, we construct a practical way to
compute OTF as a differentiable fairness regularizer that can be added to any
standard classification setting. Experiments show that OTF can be used to
achieve an improved trade-off between predictive power and fairness.
