  This paper describes a differentially private post-processing algorithm for
learning fair regressors satisfying statistical parity, addressing privacy
concerns of machine learning models trained on sensitive data, as well as
fairness concerns of their potential to propagate historical biases. Our
algorithm can be applied to post-process any given regressor to improve
fairness by remapping its outputs. It consists of three steps: first, the
output distributions are estimated privately via histogram density estimation
and the Laplace mechanism, then their Wasserstein barycenter is computed, and
the optimal transports to the barycenter are used for post-processing to
satisfy fairness. We analyze the sample complexity of our algorithm and provide
fairness guarantee, revealing a trade-off between the statistical bias and
variance induced from the choice of the number of bins in the histogram, in
which using less bins always favors fairness at the expense of error.
