# Fairness under Graph Uncertainty: Achieving Interventional Fairness with Partially Known Causal Graphs over Clusters of Variables

arXiv: https://arxiv.org/abs/2602.23611 · HTML: https://mlsanity.com/paper/2602.23611/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 49 references that are in the map.
- First posted on arXiv 27 Feb 2026.

## Builds on (most cited first, 20 of 20)

- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Path-Specific Counterfactual Fairness](https://mlsanity.com/paper/1802.08139/) (2018)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [PC-Fairness: A Unified Framework for Measuring Causality-based Fairness](https://mlsanity.com/paper/1910.12586/) (2019)
- [Local Explanations via Necessity and Sufficiency: Unifying Theory and Practice](https://mlsanity.com/paper/2103.14651/) (2021)
- [Causal Effect Identification in Cluster DAGs](https://mlsanity.com/paper/2202.12263/) (2022)
- [Achieving non-discrimination in data release](https://mlsanity.com/paper/1611.07438/) (2016)
- [Foundations of Causal Discovery on Groups of Variables](https://mlsanity.com/paper/2306.07047/) (2023)
- [Learning Structures of Bayesian Networks for Variable Groups](https://mlsanity.com/paper/1508.07753/) (2015)
- [Clustering and Structural Robustness in Causal Diagrams](https://mlsanity.com/paper/2111.04513/) (2021)
- [Vector causal inference between two groups of variables](https://mlsanity.com/paper/2209.14283/) (2022)
- [Do we become wiser with time? On causal equivalence with tiered background knowledge](https://mlsanity.com/paper/2306.01638/) (2023)
- [Interventional Fairness on Partially Known Causal Graphs: A Constrained Optimization Approach](https://mlsanity.com/paper/2401.10632/) (2024)
- [Relaxing partition admissibility in Cluster-DAGs: a causal calculus with arbitrary variable clustering](https://mlsanity.com/paper/2511.01396/) (2025)
- [Efficient least squares for estimating total effects under linearity and causal sufficiency](https://mlsanity.com/paper/2008.03481/) (2020)
- [Counterfactual Fairness Evaluation of Machine Learning Models on Educational Datasets](https://mlsanity.com/paper/2504.11504/) (2025)
- [Differentiable Pareto-Smoothed Weighting for High-Dimensional Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2404.17483/) (2024)
- [Cluster-Dags as Powerful Background Knowledge For Causal Discovery](https://mlsanity.com/paper/2512.10032/) (2025)
- [MetaCaDI: A Meta-Learning Framework for Causal Discovery from Multiple Environments with Unknown Interventions](https://mlsanity.com/paper/2510.22298/) (2025)

## Abstract (arXiv)

Algorithmic decisions about individuals require predictions that are not only accurate but also fair with respect to sensitive attributes such as gender and race. Causal notions of fairness align with legal requirements, yet many methods assume access to detailed knowledge of the underlying causal graph, which is a demanding assumption in practice. We propose a learning framework that achieves interventional fairness by leveraging a causal graph over textitclusters of variables, which is substantially easier to estimate than a variable-level graph. With possible textitadjustment cluster sets identified from such a cluster causal graph, our framework trains a prediction model by reducing the worst-case discrepancy between interventional distributions across these sets. To this end, we develop a computationally efficient barycenter kernel maximum mean discrepancy (MMD) that scales favorably with the number of sensitive attribute values. Extensive experiments show that our framework strikes a better balance between fairness and accuracy than existing approaches, highlighting its effectiveness under limited causal graph knowledge.