  Machine learning based systems are reaching society at large and in many
aspects of everyday life. This phenomenon has been accompanied by concerns
about the ethical issues that may arise from the adoption of these
technologies. ML fairness is a recently established area of machine learning
that studies how to ensure that biases in the data and model inaccuracies do
not lead to models that treat individuals unfavorably on the basis of
characteristics such as e.g. race, gender, disabilities, and sexual or
political orientation. In this manuscript, we discuss some of the limitations
present in the current reasoning about fairness and in methods that deal with
it, and describe some work done by the authors to address them. More
specifically, we show how causal Bayesian networks can play an important role
to reason about and deal with fairness, especially in complex unfairness
scenarios. We describe how optimal transport theory can be used to develop
methods that impose constraints on the full shapes of distributions
corresponding to different sensitive attributes, overcoming the limitation of
most approaches that approximate fairness desiderata by imposing constraints on
the lower order moments or other functions of those distributions. We present a
unified framework that encompasses methods that can deal with different
settings and fairness criteria, and that enjoys strong theoretical guarantees.
We introduce an approach to learn fair representations that can generalize to
unseen tasks. Finally, we describe a technique that accounts for legal
restrictions about the use of sensitive attributes.
