[Paper Review] Networked Inequality: Preferential Attachment Bias in Graph Neural Network Link Prediction

Arjun Subramonian, Levent Sagun+1 more|arXiv (Cornell University)|Sep 29, 2023

Complex Network Analysis Techniques4 citations

TL;DR

This paper identifies a previously unexplored within-group preferential attachment bias in Graph Convolutional Networks (GCNs) with symmetric normalization, where link prediction scores correlate with the geometric mean of node degrees within social groups. The authors theoretically and empirically demonstrate that this bias amplifies degree and power disparities—especially disadvantaging lower-degree individuals—propose a novel within-group fairness metric, and introduce a training-time regularization strategy that effectively reduces unfairness across citation, social, and credit networks.

ABSTRACT

Graph neural network (GNN) link prediction is increasingly deployed in citation, collaboration, and online social networks to recommend academic literature, collaborators, and friends. While prior research has investigated the dyadic fairness of GNN link prediction, the within-group (e.g., queer women) fairness and "rich get richer" dynamics of link prediction remain underexplored. However, these aspects have significant consequences for degree and power imbalances in networks. In this paper, we shed light on how degree bias in networks affects Graph Convolutional Network (GCN) link prediction. In particular, we theoretically uncover that GCNs with a symmetric normalized graph filter have a within-group preferential attachment bias. We validate our theoretical analysis on real-world citation, collaboration, and online social networks. We further bridge GCN's preferential attachment bias with unfairness in link prediction and propose a new within-group fairness metric. This metric quantifies disparities in link prediction scores within social groups, towards combating the amplification of degree and power disparities. Finally, we propose a simple training-time strategy to alleviate within-group unfairness, and we show that it is effective on citation, social, and credit networks.

Motivation & Objective

• To investigate how degree bias in network structure affects Graph Neural Network (GNN) link prediction fairness.
• To identify and analyze a previously unexplored within-group preferential attachment (PA) bias in GCNs with symmetric normalized graph filters.
• To bridge GCN’s PA bias with unfairness in link prediction by introducing a new within-group fairness metric.
• To propose and evaluate a training-time regularization strategy that mitigates within-group unfairness in link prediction.
• To validate findings across diverse real-world networks, including citation, collaboration, online social, and credit networks.

Proposed method

• Theoretical analysis shows that GCNs with symmetric normalized graph filters produce link prediction scores proportional to the geometric mean of within-group node degrees, indicating a within-group PA bias.
• A new within-group fairness metric, $\widehat{\Delta}^{(b)}$, is proposed to quantify disparities in LP scores between social groups based on degree differences.
• A training-time regularization loss, $\mathcal{L}_{\text{fair}}$, is introduced to penalize unfair LP score disparities between nodes of different degrees within the same group.
• The method is evaluated on citation (CORA, CITESEER, DBLP, PUBMED), collaboration (CS, PHYSICS), online social (LASTFMASIA, DE, EN, FR), and credit (NBA, GERMAN, DBLP-Fairness) networks.
• Experiments compare 2-layer and 4-layer GCN encoders to validate robustness of the theoretical findings across model depth.
• Theoretical predictions of LP scores are compared against actual GCN outputs using NRMSE and PCC metrics to validate the PA bias hypothesis.

Experimental results

Research questions

• RQ1 Does a GCN with symmetric normalization exhibit a within-group preferential attachment bias in link prediction?
• RQ2 How does this bias amplify degree and power imbalances in social networks, particularly in academic and collaboration settings?
• RQ3 Can a novel within-group fairness metric effectively quantify disparities in link prediction scores between social groups based on node degree?
• RQ4 To what extent can a training-time regularization strategy mitigate within-group unfairness in GCN-based link prediction?
• RQ5 Does the PA bias persist in GCNs with random walk normalization, or is it specific to symmetric normalization?

Key findings

• GCNs with symmetric normalized graph filters exhibit a within-group preferential attachment bias, where link prediction scores are proportional to the geometric mean of the degrees of the two nodes in the same social group.
• The theoretical prediction of LP scores based on degree product and feature similarity correlates strongly with actual GCN outputs, with PCC values ranging from 0.752 to 0.950 across datasets.
• The proposed fairness metric $\widehat{\Delta}^{(b)}$ effectively captures disparities in LP scores between high- and low-degree nodes within the same group, with NRMSE values below 0.06 across most datasets.
• The training-time regularization strategy reduces the fairness loss $\mathcal{L}_{\text{fair}}$ by up to 75% (e.g., from 0.122 to 0.000 in NBA, 0.028 to 0.000 in GERMAN) while maintaining or slightly improving test AUC.
• The method is effective across diverse network types: citation (CORA, DBLP), collaboration (CS, PHYSICS), online social (LASTFMASIA, EN), and credit (NBA, GERMAN) networks.
• Even with deeper 4-layer GCN encoders, the theoretical and empirical results continue to support the existence of the within-group PA bias, with comparable or improved NRMSE and PCC values.