  Despite recent advances in algorithmic fairness, methodologies for achieving
fairness with generalized linear models (GLMs) have yet to be explored in
general, despite GLMs being widely used in practice. In this paper we introduce
two fairness criteria for GLMs based on equalizing expected outcomes or
log-likelihoods. We prove that for GLMs both criteria can be achieved via a
convex penalty term based solely on the linear components of the GLM, thus
permitting efficient optimization. We also derive theoretical properties for
the resulting fair GLM estimator. To empirically demonstrate the efficacy of
the proposed fair GLM, we compare it with other well-known fair prediction
methods on an extensive set of benchmark datasets for binary classification and
regression. In addition, we demonstrate that the fair GLM can generate fair
predictions for a range of response variables, other than binary and continuous
outcomes.

Machine Learning;Machine Learning;Methodology