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Fairness-Aware Node Representation Learning

Öykü Deniz Köse, Yanning Shen

arXiv:2106.05391v1cs.LG

TL;DR

Fairness remains under-explored in graph contrastive learning, where GNN representations can reflect sensitive-attribute bias. This paper introduces fairness-guided adaptive feature masking and edge deletion, and reports improved fairness with comparable classification accuracy on real social graphs.

  • Problem

    Fairness is under-explored in graph contrastive learning, and GNN neighbor aggregation can carry sensitive-attribute correlations into representations and downstream tasks.

    Source: §1 · pp. 1–2

  • Method

    The paper introduces graph fairness concepts to guide adaptive feature masking and edge deletion for generating contrastive graph views.

    Source: §1 · p. 2, §3.3.1 · p. 4, §3.3.2 · p. 6

  • Results

    The augmentations improve fairness metrics with comparable node-classification accuracy to state-of-the-art contrastive methods; on Pokec-n, FM +p(T) reduces ∆SP by 45.12%.

    Source: §1 · p. 2, §4.2 · p. 8, §5 · p. 10

  • Takeaways & Limitations

    The augmentations are presented as applicable to studies requiring corrupted graph views, with negligible computational increase compared with existing graph augmentation schemes.

    Source: §1 · p. 2

    The schemes consider only a single sensitive attribute, and results cover two social networks because fairness graph datasets are scarce.

    Source: §5 · p. 10

Abstract

from arXiv · show

Node representation learning has demonstrated its effectiveness for various applications on graphs. Particularly, recent developments in contrastive learning have led to promising results in unsupervised node representation learning for a number of tasks. Despite the success of graph contrastive learning and consequent growing interest, fairness is largely under-explored in the field. To this end, this study addresses fairness issues in graph contrastive learning with fairness-aware graph augmentation designs, through adaptive feature masking and edge deletion. In the study, different fairness notions on graphs are introduced, which serve as guidelines for the proposed graph augmentations. Furthermore, theoretical analysis is provided to quantitatively prove that the proposed feature masking approach can reduce intrinsic bias. Experimental results on real social networks are presented to demonstrate that the proposed augmentations can enhance fairness in terms of statistical parity and equal opportunity, while providing comparable classification accuracy to state-of-the-art contrastive methods for node classification.

1 Introduction

Although graph contrastive learning achieves state-of-the-art node-classification results, fairness remains under-explored, and GNN representations can carry sensitive-attribute bias into downstream tasks. This work introduces fairness-guided adaptive graph augmentations and reports theoretical and experimental support for their use.

1 Introduction

  • Neighbor aggregation can make GNN representations correlate with sensitive attributes, causing indirect discrimination even when those attributes are not used in training.In social networks, connections between nodes with similar sensitive attributes can make their connectivity denser.Source: §1 · pp. 1–2
  • Prior fairness-aware graph contrastive augmentation targeted counterfactual fairness, while its effectiveness for other fairness metrics may be unsatisfactory.The paper contrasts this with adaptive augmentation based on centrality measures that is not fairness-aware.Source: §1 · p. 2
  • The paper introduces graph fairness concepts and adaptive feature-masking and edge-deletion augmentations, with theory and social-graph evaluations supporting reduced bias and improved fairness at comparable accuracy.The feature-masking analysis shows reduced expected correlation between sensitive attributes and nodal features versus non-adaptive masking; evaluations consider statistical parity and equal opportunity.Source: §1 · p. 2

2 Related Work

Graph representation learning includes factorization-based, random-walk-based, and GNN approaches, while contrastive learning has become a prominent unsupervised approach. Prior graph contrastive methods use graph augmentations, but the cited adaptive augmentation and fairness-aware work leave a distinction between general augmentation and fairness across metrics.

Representation learning on graphs

  • Conventional graph representation methods include factorization-based approaches using deterministic node similarity and random-walk approaches using stochastic similarity.GNNs are also used for supervised and unsupervised graph representation learning.Source: §2 · p. 2

Contrastive learning on graphs

  • Graph contrastive learning maximizes agreement across embeddings under graph augmentations and achieves state-of-the-art results across tasks including node classification, regression, and link prediction.The first node-level method maximized agreement across two corrupted graph views [30]; adaptive centrality-based augmentation builds on it, but is not fairness-aware.Source: §2 · p. 2

Fairness-aware learning on graphs

  • Fairness-aware graph learning includes random-walk, adversarial-regularization, and fair-adjacency approaches, while graph contrastive fairness work [18] targets counterfactual fairness.That augmentation may not be effective for other fairness metrics.Source: §2 · pp. 2–3

3 Fair Contrastive Learning on Graphs

The framework learns node representations from graph views designed to mitigate bias in both node features and graph topology. Adaptive feature masking targets feature–sensitive-attribute correlation, while several edge-deletion schemes address structural bias.

3.1 Preliminaries

  • The framework maps graph structure, node features, and one binary sensitive attribute to node embeddings, and its augmentation schemes can extend to multiple sensitive attributes.The learned embeddings are intended for downstream tasks such as node classification.Source: §3.1 · p. 3, §3.3.2 · p. 7

3.2 Contrastive Learning over Graphs

  • The contrastive objective makes embeddings of the same node across two graph views more similar than embeddings of other nodes.It uses cosine similarity, a learned two-layer MLP transform, and a temperature parameter.Source: §3.2 · p. 3

3.3.1 Feature Masking

  • Masking probabilities increase for features more correlated with sensitive attributes, using Pearson or Spearman coefficients and their p-values.Pearson measures linear dependence; Spearman captures higher-order dependencies.Source: §3.3.1 · p. 4
  • Adaptive feature masking has a lower expected total sample correlation between nodal features and the sensitive attribute than uniform masking, reducing a measure linked to potential discrimination.The paper defines total sample correlation as the sum of absolute feature–sensitive-attribute sample correlations.Source: §3.3.1 · pp. 4–5

3.3.2 Edge Deletion

  • Dyadic fairness sets equal edge-existence probabilities for same- and different-attribute pairs, while parity-aware deletion distinguishes the four sensitive-attribute pairings.The parity-aware criterion accounts for the actual values of the sensitive attributes.Source: §3.3.2 · pp. 5–6
  • The counterfactual edge-deletion scheme contrasts views aggregating mainly from same-attribute neighbors and different-attribute neighbors, respectively.The proposed view agreement is intended to reduce potential biased effects from information collected across groups.Source: §3.3.2 · p. 6
  • Triangle-based deletion assigns higher removal probabilities to edges in same-attribute triangles than to other same-attribute edges.The scheme uses a multiplier greater than 1 for edges in the triangle set.Source: §3.3.2 · p. 6
  • Degree-aware deletion lowers removal probabilities for edges touching low-degree nodes, potentially preserving topology and improving downstream task performance.The scheme caps edge-removal probability and uses base probabilities with the same-attribute rate greater than the different-attribute rate.Source: §3.3.2 · p. 7

4 Experiments

Experiments compare fairness-aware feature masking and edge deletion with baselines on two social-network datasets, evaluating node-classification accuracy and group fairness. The proposed combined augmentations improve fairness over baselines while maintaining similar accuracy to state-of-the-art graph contrastive methods.

4.1 Datasets and Settings

  • Experiments use Pokec-z and Pokec-n, with region as the sensitive attribute and working field as the node-classification label; accuracy, statistical parity, and equal opportunity are evaluated.The datasets contain 7,659 and 6,185 users, respectively, and each has 59 nodal features; lower ∆SP and ∆EO indicate better fairness.Source: §4.1 · p. 7, §4 · p. 7

4.2 Experimental Results

  • On Pokec-z, the degree-aware scheme combined with feature masking improves both fairness metrics by approximately 54% relative to GRACE, while incurring an accuracy loss of 0.07%.Source: §4.2 · p. 8
  • On Pokec-n, triangle-based deletion with feature masking reduces ∆SP by 45.12% and ∆EO by 39.95% with a 0.12% accuracy loss; the degree-aware combination improves them by 31.94% and 25.86% while raising accuracy by 0.26% over GRACE.Source: §4.2 · p. 8
  • The strongest scheme varies by dataset: feature masking alone is fairer than edge deletion on Pokec-n, while combining them generally yields better, more stable fairness and higher accuracy.On Pokec-n, edge-deletion schemes achieve better accuracy than feature masking.Source: §4.2 · pp. 8–9
  • The proposed degree-aware and triangle-based edge-deletion schemes combined with feature masking improve fairness over baselines with classification accuracy similar to state-of-the-art graph contrastive methods.Table 2 compares the proposed schemes with baselines.Source: §4.2 · p. 9, Table 2 · p. 9

5 Conclusions and Limitations

The paper proposes fairness-aware augmentations for graph features and topology, and reports improved fairness with comparable node-classification accuracy. Its adaptive schemes consider one sensitive attribute, and experiments use two social networks.

5 Conclusions and Limitations

  • Adaptive feature masking analytically reduces the expected total sample correlation coefficient ρ between nodal features and the sensitive attribute.Source: §5 · p. 9
  • The proposed augmentations improve fairness metrics while providing classification accuracy comparable to state-of-the-art methods for node classification.The schemes address both nodal features and graph topology.Source: §5 · pp. 9–10
  • The study considers only one sensitive attribute and reports results on two social networks.Future work is proposed to extend the schemes to multiple sensitive attributes and broaden the datasets.Source: §5 · p. 10

A.1 Proof of Proposition 1

The proof compares expected total sample correlation under adaptive and uniform feature masking. It orders feature correlations and retention probabilities, then invokes majorization to relate the sequences.

A.1 Proof of Proposition 1

  • The proof sets uniform feature-keeping probabilities to the average adaptive keeping probability for a fair comparison.Source: §A.1 · p. 13
  • Ordering absolute feature correlations from smallest to largest also orders the adaptive keeping probabilities from largest to smallest.Source: §A.1 · p. 13
  • The proof uses that the uniform sequence is majorized by any non-increasing sequence with the same sum, so the adaptive probability sequence majorizes the uniform one.The passages introduce expected-correlation expressions for both adaptive and uniform masking, but do not provide their complete formulas.Source: §A.1 · p. 13

A.2 Additional Statistics on Datasets

The dataset statistics describe edge groups by whether connected users share the sensitive attribute. Their values support the paper's claim that users in these social graphs tend to connect to users with similar attributes.

A.2 Additional Statistics on Datasets

  • Inter-group edges connect users with the same sensitive attribute, while intra-group edges connect users with different sensitive attributes; their values support a tendency toward similar-attribute connections.The reported statistics differ from the original datasets because this study uses nodes with complete region and working-field information and the largest connected graphs.Source: §A.2 · p. 14
  • Table 3 reports statistical information for the Pokec-z and Pokec-n datasets.Source: Table 3 · p. 14, §A.2 · p. 14

A.3 Computing Infrastructures

The experiments used specified software libraries for GNN-based models and five Intel Xeon Gold 6248 CPUs.

A.3 Computing Infrastructures

  • GNN-based models were trained with PyTorch 1.8.1, PyTorch Geometric 1.7.0, and NetworkX 2.5.Source: §A.3 · p. 14
  • Experiments ran on five Intel Xeon Gold 6248 CPUs.Source: §A.3 · p. 14

A.4 Hyperparameters

The appendix reports the GNN training settings and directs readers to tables for the proposed methods’ hyperparameters. Adaptive fair-augmentation parameters were selected by grid search.

A.4 Hyperparameters

  • All models use 400 epochs, Adam, a 5 × 10−4 learning rate, and 10−5 l2 weight decay.Source: §A.4 · p. 14
  • The GNN encoder uses Glorot initialization, ReLU after each GCN layer, temperature τ = 0.4, and 256-dimensional node representations on both datasets.Source: §A.4 · p. 14
  • Adaptive fair-augmentation hyperparameters are listed in Table A.4 and were selected via grid search.Source: §A.4 · p. 14, Table 4 · p. 15

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