  As machine learning powered decision-making becomes increasingly important in
our daily lives, it is imperative to strive for fairness in the underlying data
processing. We propose a pre-processing algorithm for fair data representation
via which supervised learning results in estimations of the Pareto frontier
between prediction error and statistical disparity. Particularly, the present
work applies the optimal affine transport to approach the post-processing
Wasserstein-2 barycenter characterization of the optimal fair $L^2$-objective
supervised learning via a pre-processing data deformation. Furthermore, we show
that the Wasserstein-2 geodesics from the conditional (on sensitive
information) distributions of the learning outcome to their barycenter
characterizes the Pareto frontier between $L^2$-loss and the average pairwise
Wasserstein-2 distance among sensitive groups on the learning outcome.
Numerical simulations underscore the advantages: (1) the pre-processing step is
compositive with arbitrary conditional expectation estimation supervised
learning methods and unseen data; (2) the fair representation protects the
sensitive information by limiting the inference capability of the remaining
data with respect to the sensitive data; (3) the optimal affine maps are
computationally efficient even for high-dimensional data.
