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Breaking the Dyadic Barrier: Rethinking Fairness in Link Prediction Beyond Demographic Parity

João Mattos, Debolina Halder Lina, Arlei Silva

TL;DR

This paper argues that traditional demographic parity (Delta_DP) is inadequate for fairness in link prediction, because it hides subgroup biases and ignores ranking exposure. It introduces a non-dyadic, distribution-preserving fairness framework and a ranking-aware metric, ND_KL (NDKL), to evaluate and enforce fair exposure across edge-types. The authors propose MORAL, a post-processing method that trains separate predictors for each sensitive-group edge type and greedily aggregates their outputs to match a target edge-type distribution, improving fairness without sacrificing utility. Empirical results on six real-world graphs show MORAL achieves superior fairness-utility trade-offs under ND_KL compared to a broad range of baselines. The work thus offers a practical, scalable approach to fair link prediction that accounts for both subgroup distributions and ranking exposure, with broad implications for fairness in graph-based recommendation and knowledge-graph tasks.

Abstract

Link prediction is a fundamental task in graph machine learning with applications, ranging from social recommendation to knowledge graph completion. Fairness in this setting is critical, as biased predictions can exacerbate societal inequalities. Prior work adopts a dyadic definition of fairness, enforcing fairness through demographic parity between intra-group and inter-group link predictions. However, we show that this dyadic framing can obscure underlying disparities across subgroups, allowing systemic biases to go undetected. Moreover, we argue that demographic parity does not meet desired properties for fairness assessment in ranking-based tasks such as link prediction. We formalize the limitations of existing fairness evaluations and propose a framework that enables a more expressive assessment. Additionally, we propose a lightweight post-processing method combined with decoupled link predictors that effectively mitigates bias and achieves state-of-the-art fairness-utility trade-offs.

Breaking the Dyadic Barrier: Rethinking Fairness in Link Prediction Beyond Demographic Parity

TL;DR

This paper argues that traditional demographic parity (Delta_DP) is inadequate for fairness in link prediction, because it hides subgroup biases and ignores ranking exposure. It introduces a non-dyadic, distribution-preserving fairness framework and a ranking-aware metric, ND_KL (NDKL), to evaluate and enforce fair exposure across edge-types. The authors propose MORAL, a post-processing method that trains separate predictors for each sensitive-group edge type and greedily aggregates their outputs to match a target edge-type distribution, improving fairness without sacrificing utility. Empirical results on six real-world graphs show MORAL achieves superior fairness-utility trade-offs under ND_KL compared to a broad range of baselines. The work thus offers a practical, scalable approach to fair link prediction that accounts for both subgroup distributions and ranking exposure, with broad implications for fairness in graph-based recommendation and knowledge-graph tasks.

Abstract

Link prediction is a fundamental task in graph machine learning with applications, ranging from social recommendation to knowledge graph completion. Fairness in this setting is critical, as biased predictions can exacerbate societal inequalities. Prior work adopts a dyadic definition of fairness, enforcing fairness through demographic parity between intra-group and inter-group link predictions. However, we show that this dyadic framing can obscure underlying disparities across subgroups, allowing systemic biases to go undetected. Moreover, we argue that demographic parity does not meet desired properties for fairness assessment in ranking-based tasks such as link prediction. We formalize the limitations of existing fairness evaluations and propose a framework that enables a more expressive assessment. Additionally, we propose a lightweight post-processing method combined with decoupled link predictors that effectively mitigates bias and achieves state-of-the-art fairness-utility trade-offs.

Paper Structure

This paper contains 31 sections, 1 theorem, 5 equations, 5 figures, 8 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Limitations of Demographic Parity for Fair Link Prediction
  4. Expressive Power Impact on Fairness
  5. Bias Within Edge Groups ($E_{s \text{-} s}$ vs. $E_{s' \text{-} s'}$)
  6. Example
  7. Toward Subgroup-Sensitive Fairness.
  8. Bias Across Edge Groups ($E_{\text{intra}}$ vs. $E_{\text{inter}}$)
  9. Example
  10. Distribution-Preserving and Ranking-Aware Fair Link Prediction
  11. Fair Ranking Metrics
  12. MORAL - Multi-Output Ranking Aggregation for Link Fairness
  13. Experiments
  14. Hidden Bias in Dyadic Fairness
  15. Demographic Parity Gap
  16. ...and 16 more sections

Key Result

Theorem 1

Let $\boldsymbol{\pi} = [\pi_0, \pi_1, \pi_2]$ be the target distribution over $3$ sensitive groups, with $\sum_i \pi_i = 1$, and let $\hat{\boldsymbol{\pi}}_k$ denote the empirical distribution over the top-$k$ ranked items. Under the constraint that the full ranking satisfies demographic parity (i

Figures (5)

  • Figure 1: Toy example showing how $\Delta_{DP}$ fails to distinguish subgroup bias within aggregated edge groups. Both panels depict top-10 link predictions (dashed edges) over the same graph, achieving the optimal $\Delta_{DP}$ value despite the left scenario overrepresenting $E_{s \text{-} s}$ (blue) relative to $E_{s' \text{-} s'}$ (red), while $E_{s' \text{-} s}$ (gray) is the protected group.
  • Figure 2: $\Delta_{DP}$ fails to capture exposure and subgroup proportion bias. Three models (a)–(c) output top-$10$ link predictions over a graph with original subgroup edge proportions of 50% $E_{s \text{-} s}$ (blue), 30% $E_{s' \text{-} s'}$ (red), and 20% $E_{s' \text{-} s}$ (black).
  • Figure 3: Proportions of pair types in the top-$100$ predictions by method, compared against the original graph distribution and an optimal dyadic fairness reference. Colors: $E_{s \text{-} s}$ (blue), $E_{s' \text{-} s}$ (black), and $E_{s' \text{-} s'}$ (red). In the dyadic fairness reference, purple represents the combined proportion of $E_{s' \text{-} s'}$ and $E_{s \text{-} s}$ pairs. Missing bars indicate an OOM error.
  • Figure 4: 1-WL GNN Indistinguishability in Pair Representations.This graph illustrates a structural limitation of 1-WL GNNs in distinguishing node pairs for fairness-aware link prediction. Nodes are colored by sensitive group (blue and red), with labeled nodes $v_1$, $v_2$, and $v_3$. Despite $v_2$ and$v_3$ belonging to different groups, both are structurally symmetric with respect to $v_1$. As a result, standard message-passing GNNs produce nearly identical embeddings for $(v_1, v_2)$ and $(v_1, v_3)$, failing to capture the demographic asymmetry between these node pairs. This highlights a key expressivity limitation of 1-WL GNNs for fair link prediction.
  • Figure 5: NDKL gap for optimal $\Delta_{DP}$ for all six datasets, varying $k$. The red curve denotes the worst ranking obtained with the optimal proportions of each pair type, while the black curve denotes the ranking outputted by the Algorithm \ref{['alg:greedy_dkl']}. Despite both curves obtaining the same (optimal) value of $\Delta_{DP}$ , there is a very significant gap between the NDKL measurements.

Theorems & Definitions (4)

  • Definition 1: Demographic Parity - $\Delta_{DP}$
  • Definition 2: Normalized Cumulative KL-Divergence - NDKL
  • Theorem 1
  • proof