  In spite of the high performance and reliability of deep learning algorithms
in a wide range of everyday applications, many investigations tend to show that
a lot of models exhibit biases, discriminating against specific subgroups of
the population (e.g. gender, ethnicity). This urges the practitioner to develop
fair systems with a uniform/comparable performance across sensitive groups. In
this work, we investigate the gender bias of deep Face Recognition networks. In
order to measure this bias, we introduce two new metrics, $\mathrm{BFAR}$ and
$\mathrm{BFRR}$, that better reflect the inherent deployment needs of Face
Recognition systems. Motivated by geometric considerations, we mitigate gender
bias through a new post-processing methodology which transforms the deep
embeddings of a pre-trained model to give more representation power to
discriminated subgroups. It consists in training a shallow neural network by
minimizing a Fair von Mises-Fisher loss whose hyperparameters account for the
intra-class variance of each gender. Interestingly, we empirically observe that
these hyperparameters are correlated with our fairness metrics. In fact,
extensive numerical experiments on a variety of datasets show that a careful
selection significantly reduces gender bias. The code used for the experiments
can be found at https://github.com/JRConti/EthicalModule_vMF.
