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BeMap: Balanced Message Passing for Fair Graph Neural Network

Xiao Lin, Jian Kang, Weilin Cong, Hanghang Tong

TL;DR

This paper empirically and theoretically demonstrates that message passing could amplify the bias when the 1-hop neighbors from different demographic groups are unbalanced, and proposes BeMap, a fair message passing method that leverages a balance-aware sampling strategy to balance the number of the 1-hop neighbors of each node among different demographic groups.

Abstract

Fairness in graph neural networks has been actively studied recently. However, existing works often do not explicitly consider the role of message passing in introducing or amplifying the bias. In this paper, we first investigate the problem of bias amplification in message passing. We empirically and theoretically demonstrate that message passing could amplify the bias when the 1-hop neighbors from different demographic groups are unbalanced. Guided by such analyses, we propose BeMap, a fair message passing method, that leverages a balance-aware sampling strategy to balance the number of the 1-hop neighbors of each node among different demographic groups. Extensive experiments on node classification demonstrate the efficacy of BeMap in mitigating bias while maintaining classification accuracy. The code is available at https://github.com/xiaolin-cs/BeMap.

BeMap: Balanced Message Passing for Fair Graph Neural Network

TL;DR

This paper empirically and theoretically demonstrates that message passing could amplify the bias when the 1-hop neighbors from different demographic groups are unbalanced, and proposes BeMap, a fair message passing method that leverages a balance-aware sampling strategy to balance the number of the 1-hop neighbors of each node among different demographic groups.

Abstract

Fairness in graph neural networks has been actively studied recently. However, existing works often do not explicitly consider the role of message passing in introducing or amplifying the bias. In this paper, we first investigate the problem of bias amplification in message passing. We empirically and theoretically demonstrate that message passing could amplify the bias when the 1-hop neighbors from different demographic groups are unbalanced. Guided by such analyses, we propose BeMap, a fair message passing method, that leverages a balance-aware sampling strategy to balance the number of the 1-hop neighbors of each node among different demographic groups. Extensive experiments on node classification demonstrate the efficacy of BeMap in mitigating bias while maintaining classification accuracy. The code is available at https://github.com/xiaolin-cs/BeMap.
Paper Structure (26 sections, 7 theorems, 42 equations, 3 figures, 6 tables, 1 algorithm)

This paper contains 26 sections, 7 theorems, 42 equations, 3 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Preliminaries
  2. Bias Amplification in Message Passing
  3. Empirical Evidence
  4. Theoretical Analysis
  5. BeMap: A Fair Message Passing Schema
  6. Fair Message Passing
  7. BeMap Algorithm
  8. Experiments
  9. Experimental Settings
  10. Experimental Results
  11. Conclusion
  12. Key Symbols of BeMap
  13. Proof of Lemma \ref{['lm:linear_node_embed']}
  14. Analysis on Linear GCN
  15. Stable Centroid
  16. ...and 11 more sections

Key Result

Lemma 1

(Linear decomposition of a node embedding) Suppose that Assumption asmp:exist_fair_node_emb holds. Given an input graph $\mathcal{G} = \left\{\mathcal{V}, \mathbf{A}, \mathbf{X}\right\}$ and an $L$-layer linear GCN with row normalization, we have for any $v_i \in \mathcal{V}$ and any hidden layer $l\in\left\{1, \dots, L\right\}$, where $\mathbf{t}_i^{\left(l\right)} = \widetilde{\mathbf{A}}^{l-1}

Figures (3)

  • Figure 1: The empirical evidence of bias amplification in GCN on the Pokec-z dataset. Best viewed in color. In (b), majority neighbor ratio is grouped into 10 equal-width bins with width being $0.1$, i.e., $[0, 0.1), [0.1, 0.2),\ldots,[0.9, 1.0]$.
  • Figure 2: Node classification accuracy (ACC) and AUC score (AUC) curves of linear GCN (Linear GCN) vs. nonlinear GCN (ReLU GCN) on the NBA dataset.
  • Figure 3: An illustrative example of BeMap. After BeMap, the bias residuals will move towards the fair centroid (the green point), whereas, after the vanilla message passing in GCN, they will move towards the centroid of the majority group and the minority group (the red points).

Theorems & Definitions (13)

  • Definition 1
  • Definition 2
  • Lemma 1
  • Definition 3
  • Theorem 1
  • Lemma 2
  • Theorem 2
  • Proposition 1
  • proof
  • Proposition 2
  • ...and 3 more