Towards counterfactual fairness through auxiliary variables

TL;DR

EXOC addresses the fairness-accuracy tension in counterfactual fairness by introducing exogenous-information-inspired auxiliary and control nodes within a causal framework. The method formalizes an ELBO-based latent-variable model with $K$, $S'$, and $S''$, and uses a dedicated loss $\mathcal{L}_c(S',S'')$ and a balancing parameter $\gamma$ to control information flow from sensitive attributes to the target. Compared to prior approaches like Fair-K and CLAIRE, EXOC explicitly models intrinsic properties via $S'$ and tunes their influence through $S''$, yielding tighter counterfactual fairness (lower $\text{MMD}$ and $\text{Wass}$) with minimal performance loss. Experiments on Law School and Adult datasets (real and synthetic) demonstrate robust improvements in fairness while maintaining predictive accuracy, highlighting practical potential for fair decision-making systems that must balance bias reduction with task performance.

Abstract

The challenge of balancing fairness and predictive accuracy in machine learning models, especially when sensitive attributes such as race, gender, or age are considered, has motivated substantial research in recent years. Counterfactual fairness ensures that predictions remain consistent across counterfactual variations of sensitive attributes, which is a crucial concept in addressing societal biases. However, existing counterfactual fairness approaches usually overlook intrinsic information about sensitive features, limiting their ability to achieve fairness while simultaneously maintaining performance. To tackle this challenge, we introduce EXOgenous Causal reasoning (EXOC), a novel causal reasoning framework motivated by exogenous variables. It leverages auxiliary variables to uncover intrinsic properties that give rise to sensitive attributes. Our framework explicitly defines an auxiliary node and a control node that contribute to counterfactual fairness and control the information flow within the model. Our evaluation, conducted on synthetic and real-world datasets, validates EXOC's superiority, showing that it outperforms state-of-the-art approaches in achieving counterfactual fairness. Our code is available at https://github.com/CASE-Lab-UMD/counterfactual_fairness_2025.

Figures (4)

• Figure 1: The causal models of Fair-K and EXOC. $S$ is the sensitive attribute, $\mathbf{X}$ is observed non-sensitive attributes, $Y$ is the target attribute, $K$ is the latent domain knowledge, and $S'$ and $S"$ are latent auxiliary nodes, $U$ is the exogenous variable. The solid lines represent designed causal relationships, and dashed lines mean our focused existing relationships in implementation, illustrated in \ref{['sec:exp']} (note that $U$ have existing causal relationships with every node pearl2009causal).
• Figure 2: The distribution mapping regarding $\mathcal{L}_c(S',S")$, which can be seen as a probability inference perspective of the partial causal graph in Fig. \ref{['figb']}, where blue arrows mean the distribution parity are tightened, red arrows mean loosened, the dashed line circle is the true distribution, the full line circle is the inferred distribution. Blue circles are close to true distributions, and orange circles are far from true distributions. Note that the $\gamma$ is positively related to the effect of $\mathcal{L}_c(S',S")$, so the constraint of $\mathcal{L}_c(S',S")$ in Fig \ref{['fig2a']} is tighter, in Fig \ref{['fig2b']} is looser.
• Figure 3: The ablation study on $S"$ and $\hat{Y}$
• Figure 4: The generate causal model framework, where $\mathbf{X}_1$ to $\mathbf{X}_n$ denotes the layer of the causal relationship from $S$ to the related variables. For example, the Law school dataset is a special case of the framework, where $\mathbf{X}_1$ contains $\mathbf{X}$; $\mathbf{X}_2$ contains $K$ in Fig. \ref{['fig:dag_combined']}.