  We develop a novel method for ensuring fairness in machine learning which we
term as the Renyi Fair Information Bottleneck (RFIB). We consider two different
fairness constraints - demographic parity and equalized odds - for learning
fair representations and derive a loss function via a variational approach that
uses Renyi's divergence with its tunable parameter $\alpha$ and that takes into
account the triple constraints of utility, fairness, and compactness of
representation. We then evaluate the performance of our method for image
classification using the EyePACS medical imaging dataset, showing it
outperforms competing state of the art techniques with performance measured
using a variety of compound utility/fairness metrics, including accuracy gap
and Rawls' minimal accuracy.
