  With the widespread deployment of large-scale prediction systems in
high-stakes domains, e.g., face recognition, criminal justice, etc., disparity
on prediction accuracy between different demographic subgroups has called for
fundamental understanding on the source of such disparity and algorithmic
intervention to mitigate it. In this paper, we study the accuracy disparity
problem in regression. To begin with, we first propose an error decomposition
theorem, which decomposes the accuracy disparity into the distance between
marginal label distributions and the distance between conditional
representations, to help explain why such accuracy disparity appears in
practice. Motivated by this error decomposition and the general idea of
distribution alignment with statistical distances, we then propose an algorithm
to reduce this disparity, and analyze its game-theoretic optima of the proposed
objective functions. To corroborate our theoretical findings, we also conduct
experiments on five benchmark datasets. The experimental results suggest that
our proposed algorithms can effectively mitigate accuracy disparity while
maintaining the predictive power of the regression models.
