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Algorithmic fairness involves expressing notions such as equity, orreasonable treatment, as quantifiable measures that a machine learningalgorithm can optimise. Most work in the literature to date has focused onclassification problems where the prediction is categorical, such as acceptingor rejecting a loan application. This is in part because classificationfairness measures are easily computed by comparing the rates of outcomes,leading to behaviours such as ensuring that the same fraction of eligible menare selected as eligible women. But such measures are computationally difficultto generalise to the continuous regression setting for problems such aspricing, or allocating payments. The difficulty arises from estimatingconditional densities (such as the probability density that a system willover-charge by a certain amount). For the regression setting we introducetractable approximations of the independence, separation and sufficiencycriteria by observing that they factorise as ratios of different conditionalprobabilities of the protected attributes. We introduce and train machinelearning classifiers, distinct from the predictor, as a mechanism to estimatethese probabilities from the data. This naturally leads to model agnostic,tractable approximations of the criteria, which we explore experimentally.

Fairness Measures for Regression via Probabilistic Classification