Fair Graph Machine Learning under Adversarial Missingness Processes

TL;DR

This work tackles fairness in graph neural networks when sensitive attributes may be missing under adversarial patterns. It introduces BFtS, a 3-player adversarial framework that jointly trains a GNN classifier, a sensitive-attribute predictor, and a missing-data imputer, with the imputer optimized to produce worst-case imputations for fairness while preserving accuracy. Theoretical results show the approach induces a minimax property and can drive demographic parity under the worst-case imputation; empirically BFtS yields a better fairness × accuracy trade-off than existing baselines on both synthetic and real datasets. The method operates effectively even with partial or no sensitive information, offering a robust tool for fair graph learning in realistic missing-data scenarios.

Abstract

Graph Neural Networks (GNNs) have achieved state-of-the-art results in many relevant tasks where decisions might disproportionately impact specific communities. However, existing work on fair GNNs often assumes that either sensitive attributes are fully observed or they are missing completely at random. We show that an adversarial missingness process can inadvertently disguise a fair model through the imputation, leading the model to overestimate the fairness of its predictions. We address this challenge by proposing Better Fair than Sorry (BFtS), a fair missing data imputation model for sensitive attributes. The key principle behind BFtS is that imputations should approximate the worst-case scenario for fairness -- i.e. when optimizing fairness is the hardest. We implement this idea using a 3-player adversarial scheme where two adversaries collaborate against a GNN classifier, and the classifier minimizes the maximum bias. Experiments using synthetic and real datasets show that BFtS often achieves a better fairness x accuracy trade-off than existing alternatives under an adversarial missingness process.

Figures (9)

• Figure 1: Motivation: In Figure (a), a graph machine learning algorithm is applied to decide who receives credit (positive or negative) based on a possibly missing sensitive attribute, gender (and binary only for illustrative purposes). As shown in Figure (b), traditional missing data imputation does not account for outcomes (positive/negative), and thus, their imputed values can under-represent the bias of the complete dataset---demographic parity (DP) is $0.09$ in this example. This paper proposes BFtS, an imputation method for graph data that optimizes fairness in the worst-case imputation scenario using adversarial learning, as shown in Figure (c), where DP is $0.47$.
• Figure 2: Empirical results showing that a simple degree-based adversarial missingness process is effective at minimizing the bias of an independent imputation model (GNN) compared with a random missingness process. The last column of each matrix shows the true bias in the data, and lower values show that the bias is underestimated. We also show results for our approach (BFtS) described in Section \ref{['sec::imputation']} that addresses this problem using a 3-player adversarial imputation method.
• Figure 3: Fairness–utility trade-off of BFtS on the Bail dataset as $\beta$ varies, compared to a fair adversarial model trained with complete data. Lower $\beta$ yields higher accuracy but lower fairness.
• Figure 4: 3-player framework for fair GNN training with missing data imputation (BFtS). $f_C$ generates node representations by minimizing the classification loss $\mathcal{L}_C$ (Eqn. \ref{['eqn::lc']}) and the maximizing sensitive attribute prediction loss $\mathcal{L}_A$ (Eqn. \ref{['eqn::la']}). $f_A$ predicts sensitive attributes using representations from $f_C$ by minimizing $\mathcal{L}_A$. $f_I$ predicts missing values by minimizing the imputation loss $\mathcal{L}_I$ (Eqn. \ref{['eqn::le']}) and maximizing $\mathcal{L}_A$. $\hat{y}$, $\hat{si}$, $\hat{sa}$ are predictions from $f_C$, $f_I$ and $f_A$, respectively.
• Figure 5: Performance of the methods using the Simulation dataset for different values of assortativity coefficients. In the x-axis, we plot the F1 score, and in the y-axis of the top row, we plot $1- \Delta DP$, and in the y-axis of the bottom row, we plot $1- \Delta EQOP$. The top right corner of the plot, therefore, represents a high F1 with low bias. When the assortativity is low, other methods fail to learn the node labels. With higher assortativity, though other methods learn the class labels, BFtS is less biased and has similar accuracy. Note that the X-axes have different ranges.

Theorems & Definitions (9)

• Definition 1
• Definition 2
• Theorem 1
• Theorem 2
• Theorem 3
• Corollary 1
• proof
• proof
• proof