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Learning Fair Node Representations with Graph Counterfactual Fairness

Jing Ma, Ruocheng Guo, Mengting Wan, Longqi Yang, Aidong Zhang, Jundong Li

arXiv:2201.03662v1cs.LGcs.AI

TL;DR

Existing graph counterfactual-fairness methods often omit neighbors’ sensitive attributes and causal effects on features and graph structure. The paper proposes graph counterfactual fairness and GEAR, which augments data with self- and neighbor-perturbed counterfactuals and aligns representations. Experiments on synthetic and real-world graphs report stronger fairness performance than baselines with comparable prediction performance.

  • Problem

    Existing graph counterfactual-fairness studies neglect neighbors’ sensitive attributes and may assume sensitive attributes do not causally affect other features or graph structure.

    Source: §1 · p. 2

  • Method

    GEAR generates counterfactuals by perturbing each node’s and its neighbors’ sensitive attributes, then minimizes the discrepancy between representations from original data and counterfactuals.

    Source: §1 · p. 2

  • Results

    Experiments on synthetic and real-world graphs show GEAR outperforms existing baselines on multiple fairness notions while achieving comparable downstream prediction performance.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The paper presents graph counterfactual fairness as a notion that accounts for sensitive-attribute pathways through both nodes and their neighbors.

    Source: §1 · p. 2, §6 · p. 8

    Although multiple causal models were tried, the paper reports results for only the described model and says observations were generally consistent across experiments.

    Source: §4.1 · p. 6

Abstract

from arXiv · show

Fair machine learning aims to mitigate the biases of model predictions against certain subpopulations regarding sensitive attributes such as race and gender. Among the many existing fairness notions, counterfactual fairness measures the model fairness from a causal perspective by comparing the predictions of each individual from the original data and the counterfactuals. In counterfactuals, the sensitive attribute values of this individual had been modified. Recently, a few works extend counterfactual fairness to graph data, but most of them neglect the following facts that can lead to biases: 1) the sensitive attributes of each node's neighbors may causally affect the prediction w.r.t. this node; 2) the sensitive attributes may causally affect other features and the graph structure. To tackle these issues, in this paper, we propose a novel fairness notion - graph counterfactual fairness, which considers the biases led by the above facts. To learn node representations towards graph counterfactual fairness, we propose a novel framework based on counterfactual data augmentation. In this framework, we generate counterfactuals corresponding to perturbations on each node's and their neighbors' sensitive attributes. Then we enforce fairness by minimizing the discrepancy between the representations learned from the original graph and the counterfactuals for each node. Experiments on both synthetic and real-world graphs show that our framework outperforms the state-of-the-art baselines in graph counterfactual fairness, and also achieves comparable prediction performance.

1 INTRODUCTION

Graph node representations can carry biases tied to sensitive attributes, while existing graph counterfactual-fairness methods overlook neighbors’ sensitive attributes and causal effects on features and graph structure. The paper introduces graph counterfactual fairness and GEAR, which generates counterfactuals and aligns their node representations with those from the original data.

1 INTRODUCTION

  • Biased node representations may affect high-stakes decisions such as job-applicant ranking and credit scoring.The paper gives a loan example in which an applicant’s and close contacts’ race information could affect a bank’s decision.Source: §1 · p. 1
  • Existing graph counterfactual-fairness methods overlook both neighbors’ sensitive attributes and causal effects of sensitive attributes on features and graph structure.The paper notes that these causal relationships can shape predictions and real-world social relations.Source: §1 · p. 2
  • GEAR generates self- and neighbor-perturbed counterfactuals, then uses a Siamese network to minimize the discrepancy between their representations and those from the original subgraph.Its pipeline also prunes each node’s causal-model range to an ego-centric subgraph of influential neighbors.Source: §1 · p. 2
  • The proposed graph counterfactual fairness notion considers biases from each node’s and its neighbors’ sensitive attributes, including their causal effects on other variables.The introduction identifies features and graph structure as examples of those other variables.Source: §1 · p. 2
  • The experiments report that GEAR outperforms existing baselines on multiple fairness notions while achieving comparable downstream prediction performance.The introduction summarizes experiments on synthetic and real-world graphs.Source: §1 · p. 2

2 PROBLEM DEFINITION

The section defines graph counterfactual fairness by comparing each node’s representations across counterfactual assignments of all nodes’ sensitive attributes, allowing features and graph structure to vary. It contrasts this with an earlier graph criterion that changes only the node’s own sensitive attribute while holding everything else fixed.

Notation and assumptions

  • The setup assumes an undirected, unweighted graph and one binary sensitive attribute per node, included in that node’s features, while noting extensions to directed, weighted, multivariate, or continuous settings.Source: §2 · p. 2

Node representations

  • An encoder maps graph features and adjacency into node representations, which can serve downstream tasks including node classification, link prediction, and graph classification.Source: §2 · p. 3

Existing graph criterion

  • The earlier graph criterion changes only node i’s sensitive attribute and holds everything else fixed, omitting other nodes’ effects and assuming no effects on other features or graph structure.Source: §2 · p. 3

Graph counterfactual fairness

  • Graph counterfactual fairness requires each node’s representation distributions to match across arbitrary sensitive-attribute assignments for all nodes, with features and graph structure counterfactually changed.Counterfactual features and adjacency are defined relative to the original data and graph structure.Source: §2 · p. 3

Objective

  • The stated goal is to learn representations toward graph counterfactual fairness while maintaining good prediction performance.Source: §2 · p. 3

3 THE PROPOSED FRAMEWORK — GEAR

GEAR combines context-subgraph generation, counterfactual augmentation, and fair representation learning to reduce differences between each node’s original and counterfactual representations. Its subgraphs perturb the central node’s and neighbors’ sensitive attributes before the representations are aligned.

3.1 Subgraph Generation

  • Personalized PageRank scores select each central node’s top-k context, based on the assumption that nodes outside that context have low dependency on it.The context includes the central node and its nearest neighbors; the authors expect it to retain enough graph information for representation learning and counterfactual augmentation.Source: §3.1 · pp. 3–4

3.2 Counterfactual Data Augmentation

  • A pretrained GraphVAE reconstructs subgraphs from latent embeddings and sensitive attributes, while an adversarial constraint reduces dependence between embeddings and neighboring sensitive-attribute summaries.The assumed causal model treats sensitive attributes as exogenous and as influencing node features, graph structure, and labels.Source: §3.2 · p. 4
  • GEAR generates counterfactual subgraphs by perturbing the central node’s sensitive attribute and by randomly perturbing attributes of other nodes in its context.The number of neighbor-perturbation samples is controlled by C.Source: §3.2 · pp. 4–5

3.3 Fair Representation Learning

  • Siamese encoders represent original and counterfactual subgraphs, and GEAR minimizes distances between representations of the same central node, weighting neighbor perturbations with λ_s.An aggregator combines representations from sampled counterfactual subgraphs.Source: §3.3 · p. 5
  • A supervised prediction loss trains representations for node classification, and the framework can also extend to tasks such as link prediction.The overall objective also weights the graph counterfactual fairness constraint and L2 regularization.Source: §3.3 · p. 5

4 EXPERIMENTS

Experiments compare GEAR’s prediction and fairness performance on synthetic and real-world graphs, then examine encoder choices, parameter sensitivity, and component ablations. The reported results favor GEAR on fairness while maintaining competitive prediction performance.

4.1 Datasets

  • Experiments use a synthetic graph with a manipulable causal model and two real-world graphs, Bail and Credit defaulter, with race and age as sensitive attributes, respectively.The synthetic data-generation process includes sensitive-attribute effects on features, graph structure, and labels.Source: §4 · p. 5, §4.1 · pp. 5–6

4.3 Prediction Performance and Fairness

  • GEAR matches state-of-the-art node representation methods in prediction, surpasses all fair representation baselines in prediction, and leads them on δCF and R².It also performs well on ΔEO and ΔDP.Source: Table 3 · p. 6, §4.3 · pp. 7–8

4.1 Datasets

  • For real-world evaluation, counterfactuals are generated using a fitted causal model; although multiple models were tried, only one model’s results are shown.The authors report that observations were generally consistent across the experiments with different causal models.Source: §4.1 · p. 6

4.5 Ablation Study

  • Every tested GEAR ablation performs worse than the full model on fairness, supporting the effectiveness of its components.Variants remove self-perturbations, neighbor-perturbations, all perturbations, or counterfactual augmentation.Source: Table 4 · p. 7, §4.5 · p. 8

4.2 Experiment Settings

  • Graph counterfactual fairness is evaluated by perturbing sensitive attributes at 0%, 50%, or 100% of nodes and averaging the rate of prediction flips; R² measures prediction dependence on neighboring sensitive attributes.Prediction is also evaluated with accuracy, F1-score, and AUROC.Source: §4.2 · pp. 6–7

4.4 Model Structure & Parameter Study

  • On Bail, GraphSAGE achieves the best performance among the tested subgraph encoders, while all encoders perform well on prediction and fairness.The authors report consistent observations across other datasets.Source: Figure 3 · p. 7, §4.4 · p. 8
  • Larger λ and λs improve fairness with a slight prediction-performance sacrifice; larger subgraphs improve fairness less beyond size 20, and more neighbor perturbations improve prediction fairness.The parameter study varies λ, λs, subgraph size k, and the number of neighbor perturbations C on Bail.Source: Figure 4 · p. 7, §4.4 · p. 8

5 RELATED WORK

Prior graph-fairness work includes statistical approaches to node representations and a smaller set extending counterfactual fairness to graphs. The paper identifies unaddressed causal pathways involving neighbors and effects of sensitive attributes on features and graph structure.

5 RELATED WORK

  • Graph representation methods encode node attributes and graph structure; subgraph-based methods use central-node and sampled-subgraph correlations to capture regional structure and improve scalability.The passage names GCNs, VGAEs, GraphSAGE, SDNE, and several subgraph-based methods.Source: §5 · p. 8
  • Many graph fairness methods target statistical dependence between sensitive attributes and predictions, often using adversarial learning to make representations uninformative about those attributes.The passage distinguishes these methods from approaches that account for sensitive attributes’ causal effects on features, graph structure, or labels.Source: §5 · p. 8
  • Only a few works extend counterfactual fairness to graphs, and the cited approaches generally omit neighboring nodes’ sensitive attributes and sensitive-attribute effects on other features and graph structure.Source: §5 · p. 8

6 CONCLUSION

GEAR introduces graph counterfactual fairness and learns node representations by augmenting data with counterfactuals, aiming to preserve representation similarity across the original data and counterfactuals.

6 CONCLUSION

  • GEAR augments data with interventions on different nodes’ sensitive attributes and maximizes similarity between representations from original data and counterfactuals.Experiments on synthetic and real-world graphs validate effectiveness for fairness and prediction performance.Source: §6 · p. 8

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