  Machine Learning techniques have become pervasive across a range of different
applications, and are now widely used in areas as disparate as recidivism
prediction, consumer credit-risk analysis and insurance pricing. The prevalence
of machine learning techniques has raised concerns about the potential for
learned algorithms to become biased against certain groups. Many definitions
have been proposed in the literature, but the fundamental task of reasoning
about probabilistic events is a challenging one, owing to the intractability of
inference.
  The focus of this paper is taking steps towards the application of tractable
models to fairness. Tractable probabilistic models have emerged that guarantee
that conditional marginal can be computed in time linear in the size of the
model. In particular, we show that sum product networks (SPNs) enable an
effective technique for determining the statistical relationships between
protected attributes and other training variables. If a subset of these
training variables are found by the SPN to be independent of the training
attribute then they can be considered `safe' variables, from which we can train
a classification model without concern that the resulting classifier will
result in disparate outcomes for different demographic groups.
  Our initial experiments on the `German Credit' data set indicate that this
processing technique significantly reduces disparate treatment of male and
female credit applicants, with a small reduction in classification accuracy
compared to state of the art. We will also motivate the concept of "fairness
through percentile equivalence", a new definition predicated on the notion that
individuals at the same percentile of their respective distributions should be
treated equivalently, and this prevents unfair penalisation of those
individuals who lie at the extremities of their respective distributions.
