  Most work in algorithmic fairness to date has focused on discrete outcomes,
such as deciding whether to grant someone a loan or not. In these
classification settings, group fairness criteria such as independence,
separation and sufficiency can be measured directly by comparing rates of
outcomes between subpopulations. Many important problems however require the
prediction of a real-valued outcome, such as a risk score or insurance premium.
In such regression settings, measuring group fairness criteria is
computationally challenging, as it requires estimating information-theoretic
divergences between conditional probability density functions. This paper
introduces fast approximations of the independence, separation and sufficiency
group fairness criteria for regression models from their (conditional) mutual
information definitions, and uses such approximations as regularisers to
enforce fairness within a regularised risk minimisation framework. Experiments
in real-world datasets indicate that in spite of its superior computational
efficiency our algorithm still displays state-of-the-art accuracy/fairness
tradeoffs.
