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.

Originality: -Although the Hardt paper has suggested the use of this approach, the paper claims that it's the first to actually show this is indeed possible. Quality: -The assumptions made about the model are very well justified. The discussion after each assumption provided the context as to why the assumption makes sense and why the assumption is needed to study their model. These discussion as a result provided very good intuition and set up the stage for the proof. Clarity: -Overall, the paper have a very smooth flow, whether it be discussion of their assumptions or their remarks.

Three reviewers who are all good experts for this paper found the paper interesting, novel, compelling, and well-written. With such a difficult topic as fairness, it was particularly helpful that the authors were able to discuss their assumptions, results, and proofs so clearly, and that definitely adds value to the work. The authors' response was appreciated and was found to be helpful, but reviewers expressed some concern in discussion about adding too many new results they didn't have a chance to review, so while we hope the authors can address some of the reviewers suggestions in the final paper, they are encouraged not to add too much stuff that wasn't reviewed, but instead to consider expanding on some of that for a follow-on submission.

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.

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.