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Causal Fairness under Unobserved Confounding: A Neural Sensitivity Framework
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Derives sharp bounds on path-specific counterfactual fairness effects (DE, IE, SE) under unobserved confounding via a generalized marginal sensitivity model, and trains a neural fair predictor constrained by these worst-case bounds.
Problem
Causal fairness metrics (path-specific counterfactual direct, indirect, and spurious effects) are not identifiable from observational data when unobserved confounding exists, so fair predictions may be unfair in practice.
Approach
Unnest nested counterfactual fairness effects into identifiable terms and single-intervention effects, bound the latter with a generalized marginal sensitivity model, and use these worst-case bounds as augmented-Lagrangian constraints when training a neural predictor.
Key results
- On synthetic U_DE with confounding level 2, the fair robust model reduces DE bounds to about [0.00, 0.01] versus [0.05, 0.06] for fair naive and [0.06, 0.14] for the standard model.
- Bounds from the proposed sensitivity analysis contain the oracle causal effect once the sensitivity parameter is sufficiently large.
- On the prison sentence case study, the standard model assigns much longer sentences to non-white offenders, while the fair robust model assigns similar lengths.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Account for unobserved confounding in fairness constraints rather than using the naïve unconfounded fairness objective | Fair robust versus Fair naïve · Synthetic U_DE (Φ = 2) | Path-specific causal fairness bounds | Helped |
| Add causal fairness constraints that assume no unobserved confounding | Standard model · Synthetic U_DE (Φ = 2) | Path-specific causal fairness | Helped |
| Train without causal fairness constraints | Fair prediction model · Synthetic U_DE (Φ = 2) | Path-specific causal fairness | Hurt |
Limitations
- Restricted to discrete mediators and confounders with binary sensitive attribute in the main theorem
- Sensitivity parameter Gamma must be chosen from domain knowledge or heuristics
- Experiments limited to one synthetic setting per confounding type and one real-world case study without ground truth
Experimental setup
Datasets: Synthetic datasets (U_DE and U_IE settings) US Survey of Prison Inmates
Benchmarks: Synthetic datasets U_DE and U_IE US Survey of Prison Inmates
Metrics: upper and lower bounds on DE, IE, SE path-specific causal fa prediction loss
Baselines: Standard model Fair naive model
Builds on: generalized marginal sensitivity model marginal sensitivity model path-specific counterfactual fairness augmented Lagrangian
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