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Towards counterfactual fairness through auxiliary variables
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Proposes EXOC, a causal framework that instantiates exogenous variables as auxiliary node S' and control node S'' to improve counterfactual fairness while controlling the fairness-accuracy trade-off on Law School and Adult.
Problem
Counterfactual fairness methods usually treat sensitive attributes as having no causal parents and ignore intrinsic information in sensitive features, which hurts accuracy when trying to be fair.
Approach
Instantiate the exogenous variable U as a controllable auxiliary node S' that mediates between S and Y, and add a control node S'' tied to S' by an L2 loss (within an ELBO-trained latent model) so that a weight gamma regulates the information flow from S and K to Y, trading fairness against accuracy.
Key results
- On synthetic Law School, EXOC reaches RMSE 0.874 and MMD 3.824, versus Fair-K RMSE 0.894 and MMD 4.313.
- On synthetic Adult, EXOC reaches accuracy 0.760 and MMD 2.958, versus Fair-K accuracy 0.745 and MMD 3.597.
- On real-world Adult, EXOC reaches accuracy 0.748 and MMD 3.891, versus Fair-K accuracy 0.727 and MMD 4.381.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| introduce EXOC instead of Fair-K | EXOC · Synthetic Law school | MMD: 4.313_{\pm 0.393} -> 3.824_{\pm 0.553} | Helped |
| introduce EXOC instead of Fair-K | EXOC · Synthetic Adult | MMD: 3.597_{\pm 0.256} -> 2.958_{\pm 0.124} | Helped |
| introduce EXOC instead of Fair-K | EXOC · Law school | MMD: 5.341_{\pm 0.412} -> 4.739_{\pm 0.553} | Helped |
| introduce EXOC instead of Fair-K | EXOC · Adult | MMD: 4.381_{\pm 0.214} -> 3.891_{\pm 0.095} | Helped |
| increase γ from 1 to 2 (ablation) | EXOC · Synthetic Law school | MMD: 4.489_{\pm 0.571} -> 1.342_{\pm 0.121} | Helped |
| increase γ from 1 to 2 (ablation) | EXOC · Synthetic Law school | RMSE: 0.875_{\pm 0.006} -> 0.909_{\pm 0.003} | Hurt |
| increase γ from 1 to 2 (ablation) | EXOC · Synthetic Adult | MMD: 3.532_{\pm 0.283} -> 1.792_{\pm 0.074} | Helped |
| increase γ from 1 to 2 (ablation) | EXOC · Synthetic Adult | Accuracy: 0.765_{\pm 0.006} -> 0.746_{\pm 0.006} | Hurt |
| use S'' rather than Ŷ in the custom loss (ablation) | EXOC · Synthetic Law school | RMSE: around 0.02 RMSE decrease | Helped |
| use S'' rather than Ŷ in the custom loss (ablation) | EXOC · Synthetic Adult | Accuracy: around 0.02 Accuracy increase | Helped |
Limitations
- Evaluated only on two tabular datasets with synthetic counterfactuals generated by a VAE.
- Theoretical analysis relies on linear-Gaussian assumptions and informal KL/causal-intensity arguments.
- Fairness gains on real-world data are smaller than on synthetic data; Law School MMD of EXOC (4.739) is close to Fair-K (5.341) with overlapping variance.
Experimental setup
Datasets: Law School Adult
Benchmarks: Law School Adult
Metrics: RMSE MAE Accuracy MMD Wasserstein-1 distance
Baselines: Constant predictor Full predictor Unaware predictor Fair-K CLAIRE
Builds on: Fair-K CLAIRE counterfactual fairness ELBO maximum mean discrepancy
Closest papers by meaning
- Causal Bias Detection in Generative Artifical Intelligence (NeurIPS 2026 · similarity 0.89)
- Fairness-Accuracy Trade-Offs: A Causal Perspective (AAAI 2025 · similarity 0.88)
- FairPFN: A Tabular Foundation Model for Causal Fairness (ICML 2025 · similarity 0.88)
- Counterfactual Fairness by Combining Factual and Counterfactual Predictions (NeurIPS 2024 · similarity 0.87)
- Interventional Fairness on Partially Known Causal Graphs: A Constrained Optimization Approach (ICLR 2024 · similarity 0.87)
- Causal Fairness under Unobserved Confounding: A Neural Sensitivity Framework (ICLR 2024 · similarity 0.86)
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