  Algorithms are now routinely used to make consequential decisions that affect
human lives. Examples include college admissions, medical interventions or law
enforcement. While algorithms empower us to harness all information hidden in
vast amounts of data, they may inadvertently amplify existing biases in the
available datasets. This concern has sparked increasing interest in fair
machine learning, which aims to quantify and mitigate algorithmic
discrimination. Indeed, machine learning models should undergo intensive tests
to detect algorithmic biases before being deployed at scale. In this paper, we
use ideas from the theory of optimal transport to propose a statistical
hypothesis test for detecting unfair classifiers. Leveraging the geometry of
the feature space, the test statistic quantifies the distance of the empirical
distribution supported on the test samples to the manifold of distributions
that render a pre-trained classifier fair. We develop a rigorous hypothesis
testing mechanism for assessing the probabilistic fairness of any pre-trained
logistic classifier, and we show both theoretically as well as empirically that
the proposed test is asymptotically correct. In addition, the proposed
framework offers interpretability by identifying the most favorable
perturbation of the data so that the given classifier becomes fair.
