Fairness-Aware Optimal Graph Filter Design

Abstract

Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently. However, it has been demonstrated that ML over graphs amplifies the already existing bias towards certain under-represented groups in various decision-making problems due to the information aggregation over biased graph structures. Faced with this challenge, here we take a fresh look at the problem of bias mitigation in graph-based learning by borrowing insights from graph signal processing. Our idea is to introduce predesigned graph filters within an ML pipeline to reduce a novel unsupervised bias measure, namely the correlation between sensitive attributes and the underlying graph connectivity. We show that the optimal design of said filters can be cast as a convex problem in the graph spectral domain. We also formulate a linear programming (LP) problem informed by a theoretical bias analysis, which attains a closed-form solution and leads to a more efficient fairness-aware graph filter. Finally, for a design whose degrees of freedom are independent of the input graph size, we minimize the bias metric over the family of polynomial graph convolutional filters. Our optimal filter designs offer complementary strengths to explore favorable fairness-utility-complexity tradeoffs. For performance evaluation, we conduct extensive and reproducible node classification experiments over real-world networks. Our results show that the proposed framework leads to better fairness measures together with similar utility compared to state-of-the-art fairness-aware baselines.