SPARC: Scalable Path-Specific Counterfactual Fairness via Causal Conditional Independence

Artificial-intelligence systems are becoming ubiquitous in society, yet their predictions typically inherit biases with respect to protected attributes such as race, gender, or age. Classical fairness notions, most notably Statistical Parity (SP), demand that predictions be independent of the protected attributes, but are overly restrictive when these attributes influence mediating variables that are considered business necessities. Recent causal formulations relax SP by distinguishing allowed from not-allowed causal paths and by complementing SP with Predictive Parity (PP), requiring the predictor to replicate the legitimate influence of business-necessities. Existing path-based definitions are mainly practical when applied to categorical attributes. This paper introduces a new framework for fairness in structural causal models that is tailored to continuous protected attributes. We formalize SP and PP through path-specific partial derivatives, establish conditions under which these criteria coincide with prior causal definitions, and characterize when a fair predictor, one that satisfies SP along not-allowed paths while achieving PP along allowed paths, exists. Building on this theory, we propose a fair tuning algorithm that either constructs such a predictor or, when not possible, allows for a trade-off between SP and PP. We present experiments on simulated and real data to evaluate our proposal, compare it with previously proposed methods, and show that it performs better when PP is considered.

We consider the problem of learning a counterfactually fair regressor. We adopt a causal uncertainty view in which counterfactual fairness is defined with resampled noise. We focus on obtaining theoretical fairness guarantees for a new post-processing estimator. We begin by showing that counterfactual fairness is equivalent to satisfying demographic parity conditional on the latent variable. This allows us to provide a closed-form expression of the optimal fair regressor via a barycentric quantile map. In order to handle continuous latent variables, we propose a discretized post-processing method. Then, under mild regularity assumptions, we prove high-probability finite-sample fairness guarantees for our estimator, providing an unfairness decay at rate $\tilde O(n^{-1/3})$, and establishing a matching risk bound of order $\tilde O(n^{-1/3})$. We provide a matching lower bound on the excess risk of almost fair predictions. Finally, we extend our results to the setting of relaxed counterfactual fairness. We validate our approach on real-world and synthetic data.

Deep learning models for medical diagnosis frequently exhibit substantial performance disparities across sensitive subgroups (e.g., race, sex), even when average accuracy is high. While generative data augmentation offers a route to mitigate this, existing strategies are suboptimal; they typically address only one or two dependency channels between sensitive attributes and image features. We formalize the medical image formation process via a structural causal model, revealing that sensitive attributes actually influence image content through four distinct pathways-a structural complexity neglected by prior works. Based on this insight, we introduce CIPHER (Causal Intervention Pathways for Healthcare Equity and Robustness), a framework designed to systematically intervene on all four causal paths. To achieve this, CIPHER utilizes a diffusion backbone equipped with classifier-free guidance and null-text inversion. This technical design enables the faithful reconstruction of patient-specific anatomy while allowing for the precise, editable synthesis of counterfactuals required to break sensitive dependency chains. We tested CIPHER using chest X-ray and dermoscopy benchmarks across both standard and shifted data distributions. By employing a multi-pathway intervention strategy, our model reduced worst-group disparities by an average of 35.8% compared to disease-conditioned synthesis baselines, while also improving total diagnostic accuracy