Achieving Utility, Fairness, and Compactness via Tunable Information Bottleneck Measures

Designing machine learning algorithms that are accurate yet fair, not discriminating based on any sensitive attribute, is of paramount importance for society to accept AI for critical applications. In this article, we propose a novel fair representation learning method termed the R\'enyi Fair Information Bottleneck Method (RFIB) which incorporates constraints for utility, fairness, and compactness of representation, and apply it to image classification. A key attribute of our approach is that we consider - in contrast to most prior work - both demographic parity and equalized odds as fairness constraints, allowing for a more nuanced satisfaction of both criteria. Leveraging a variational approach, we show that our objectives yield a loss function involving classical Information Bottleneck (IB) measures and establish an upper bound in terms of the R\'enyi divergence of order $\alpha$ on the mutual information IB term measuring compactness between the input and its encoded embedding. Experimenting on three different image datasets (EyePACS, CelebA, and FairFace), we study the influence of the $\alpha$ parameter as well as two other tunable IB parameters on achieving utility/fairness trade-off goals, and show that the $\alpha$ parameter gives an additional degree of freedom that can be used to control the compactness of the representation. We evaluate the performance of our method using various utility, fairness, and compound utility/fairness metrics, showing that RFIB outperforms current state-of-the-art approaches.