Analyzing the Effect of Sampling in GNNs on Individual Fairness

Graph neural network (GNN) based methods have saturated the field of recommender systems. The gains of these systems have been significant, showing the advantages of interpreting data through a network structure. However, despite the noticeable benefits of using graph structures in recommendation tasks, this representational form has also bred new challenges which exacerbate the complexity of mitigating algorithmic bias. When GNNs are integrated into downstream tasks, such as recommendation, bias mitigation can become even more difficult. Furthermore, the intractability of applying existing methods of fairness promotion to large, real world datasets places even more serious constraints on mitigation attempts. Our work sets out to fill in this gap by taking an existing method for promoting individual fairness on graphs and extending it to support mini-batch, or sub-sample based, training of a GNN, thus laying the groundwork for applying this method to a downstream recommendation task. We evaluate two popular GNN methods: Graph Convolutional Network (GCN), which trains on the entire graph, and GraphSAGE, which uses probabilistic random walks to create subgraphs for mini-batch training, and assess the effects of sub-sampling on individual fairness. We implement an individual fairness notion called \textit{REDRESS}, proposed by Dong et al., which uses rank optimization to learn individual fair node, or item, embeddings. We empirically show on two real world datasets that GraphSAGE is able to achieve, not just, comparable accuracy, but also, improved fairness as compared with the GCN model. These finding have consequential ramifications to individual fairness promotion, GNNs, and in downstream form, recommender systems, showing that mini-batch training facilitate individual fairness promotion by allowing for local nuance to guide the process of fairness promotion in representation learning.