Leveraging labeled and unlabeled data for consistent fair binary classification

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.