  We study the problem of fair binary classification using the notion of Equal
Opportunity. It requires the true positive rate to distribute equally across
the sensitive groups. Within this setting we show that the fair optimal
classifier is obtained by recalibrating the Bayes classifier by a
group-dependent threshold. We provide a constructive expression for the
threshold. This result motivates us to devise a plug-in classification
procedure based on both unlabeled and labeled datasets. While the latter is
used to learn the output conditional probability, the former is used for
calibration. The overall procedure can be computed in polynomial time and it is
shown to be statistically consistent both in terms of the classification error
and fairness measure. Finally, we present numerical experiments which indicate
that our method is often superior or competitive with the state-of-the-art
methods on benchmark datasets.
