  We study Individual Fairness (IF) for Bayesian neural networks (BNNs).
Specifically, we consider the $\epsilon$-$\delta$-individual fairness notion,
which requires that, for any pair of input points that are $\epsilon$-similar
according to a given similarity metrics, the output of the BNN is within a
given tolerance $\delta>0.$ We leverage bounds on statistical sampling over the
input space and the relationship between adversarial robustness and individual
fairness to derive a framework for the systematic estimation of
$\epsilon$-$\delta$-IF, designing Fair-FGSM and Fair-PGD as
global,fairness-aware extensions to gradient-based attacks for BNNs. We
empirically study IF of a variety of approximately inferred BNNs with different
architectures on fairness benchmarks, and compare against deterministic models
learnt using frequentist techniques. Interestingly, we find that BNNs trained
by means of approximate Bayesian inference consistently tend to be markedly
more individually fair than their deterministic counterparts.
