  The issue of fairness in machine learning models has recently attracted a lot
of attention as ensuring it will ensure continued confidence of the general
public in the deployment of machine learning systems. We focus on mitigating
the harm incurred by a biased machine learning system that offers better
outputs (e.g. loans, job interviews) for certain groups than for others. We
show that bias in the output can naturally be controlled in probabilistic
models by introducing a latent target output. This formulation has several
advantages: first, it is a unified framework for several notions of group
fairness such as Demographic Parity and Equality of Opportunity; second, it is
expressed as a marginalisation instead of a constrained problem; and third, it
allows the encoding of our knowledge of what unbiased outputs should be.
Practically, the second allows us to avoid unstable constrained optimisation
procedures and to reuse off-the-shelf toolboxes. The latter translates to the
ability to control the level of fairness by directly varying fairness target
rates. In contrast, existing approaches rely on intermediate, arguably
unintuitive, control parameters such as covariance thresholds.
