  Algorithmic fairness involves expressing notions such as equity, or
reasonable treatment, as quantifiable measures that a machine learning
algorithm can optimise. Most work in the literature to date has focused on
classification problems where the prediction is categorical, such as accepting
or rejecting a loan application. This is in part because classification
fairness measures are easily computed by comparing the rates of outcomes,
leading to behaviours such as ensuring that the same fraction of eligible men
are selected as eligible women. But such measures are computationally difficult
to generalise to the continuous regression setting for problems such as
pricing, or allocating payments. The difficulty arises from estimating
conditional densities (such as the probability density that a system will
over-charge by a certain amount). For the regression setting we introduce
tractable approximations of the independence, separation and sufficiency
criteria by observing that they factorise as ratios of different conditional
probabilities of the protected attributes. We introduce and train machine
learning classifiers, distinct from the predictor, as a mechanism to estimate
these probabilities from the data. This naturally leads to model agnostic,
tractable approximations of the criteria, which we explore experimentally.
