Prior Signal Editing for Graph Filter Posterior Fairness Constraints

Graph filters are an emerging paradigm that systematizes information propagation in graphs as transformation of prior node values, called graph signals, to posterior scores. In this work, we study the problem of mitigating disparate impact, i.e. posterior score differences between a protected set of sensitive nodes and the rest, while minimally editing scores to preserve recommendation quality. To this end, we develop a scheme that respects propagation mechanisms by editing graph signal priors according to their posteriors and node sensitivity, where a small number of editing parameters can be tuned to constrain or eliminate disparate impact. We also theoretically explain that coarse prior editing can locally optimize posteriors objectives thanks to graph filter robustness. We experiment on a diverse collection of 12 graphs with varying number of nodes, where our approach performs equally well or better than previous ones in minimizing disparate impact and preserving posterior AUC under fairness constraints.