Graph filters that transform prior node values to posterior scores via edge propagation often support graph mining tasks affecting humans, such as recommendation and ranking. Thus, it is important to make them fair in terms of satisfying statistical parity constraints between groups of nodes (e.g., distribute score mass between genders proportionally to their representation). To achieve this while minimally perturbing the original posteriors, we introduce a filter-aware universal approximation framework for posterior objectives. This defines appropriate graph neural networks trained at runtime to be similar to filters but also locally optimize a large class of objectives, including fairness-aware ones. Experiments on a collection of 8 filters and 5 graphs show that our approach performs equally well or better than alternatives in meeting parity constraints while preserving the AUC of score-based community member recommendation and creating minimal utility loss in prior diffusion.

翻译：通过边传播将先验节点值转换为后验分数的图滤波通常支持影响人类的图挖掘任务，例如推荐和排序。因此，在满足节点组间统计均等约束（例如，按群体比例分配性别间的分数质量）方面使其公平至关重要。为在最小程度扰动原始后验分布的同时实现这一目标，我们引入了一种面向后验目标的滤波感知通用近似框架。该框架定义了适当的图神经网络，在运行时经过训练以近似滤波行为，同时能够局部优化包括公平性目标在内的大类目标函数。在涵盖8种滤波器和5个图结构的实验表明：我们的方法在满足均等约束方面表现等同或优于替代方案，同时能够保持基于分数的社区成员推荐AUC值，并在先验扩散过程中实现最小效用损失。