# Interventional Fairness on Partially Known Causal Graphs: A Constrained Optimization Approach

arXiv: https://arxiv.org/abs/2401.10632 · HTML: https://mlsanity.com/paper/2401.10632/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 84 references that are in the map.
- First posted on arXiv 19 Jan 2024.

## Builds on (most cited first, 29 of 29)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Avoiding Discrimination through Causal Reasoning](https://mlsanity.com/paper/1706.02744/) (2017)
- [Path-Specific Counterfactual Fairness](https://mlsanity.com/paper/1802.08139/) (2018)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Fair Inference On Outcomes](https://mlsanity.com/paper/1705.10378/) (2017)
- [Inherent Tradeoffs in Learning Fair Representations](https://mlsanity.com/paper/1906.08386/) (2019)
- [Why Is My Classifier Discriminatory?](https://mlsanity.com/paper/1805.12002/) (2018)
- [Discrimination in Online Ad Delivery](https://mlsanity.com/paper/1301.6822/) (2013)
- [Permutation-based Causal Inference Algorithms with Interventions](https://mlsanity.com/paper/1705.10220/) (2017)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [A causal framework for discovering and removing direct and indirect discrimination](https://mlsanity.com/paper/1611.07509/) (2016)
- [PC-Fairness: A Unified Framework for Measuring Causality-based Fairness](https://mlsanity.com/paper/1910.12586/) (2019)
- [On the relation between accuracy and fairness in binary classification](https://mlsanity.com/paper/1505.05723/) (2015)
- [Fairness in Algorithmic Decision Making: An Excursion Through the Lens of Causality](https://mlsanity.com/paper/1903.11719/) (2019)
- [The Fairness-Accuracy Pareto Front](https://mlsanity.com/paper/2008.10797/) (2020)
- [Causal Feature Selection for Algorithmic Fairness](https://mlsanity.com/paper/2006.06053/) (2020)
- [Probabilistic Evaluation of Sequential Plans from Causal Models with Hidden Variables](https://mlsanity.com/paper/1302.4977/) (2013)
- [Estimating the effect of joint interventions from observational data in sparse high-dimensional settings](https://mlsanity.com/paper/1407.2451/) (2014)
- [Counterfactual Fairness with Partially Known Causal Graph](https://mlsanity.com/paper/2205.13972/) (2022)
- [On Discrimination Discovery and Removal in Ranked Data using Causal Graph](https://mlsanity.com/paper/1803.01901/) (2018)
- [Fairness With Minimal Harm: A Pareto-Optimal Approach For Healthcare](https://mlsanity.com/paper/1911.06935/) (2019)
- [Minimal enumeration of all possible total effects in a Markov equivalence class](https://mlsanity.com/paper/2010.08611/) (2020)
- [Size of Interventional Markov Equivalence Classes in Random DAG Models](https://mlsanity.com/paper/1903.02054/) (2019)
- [Testing Identifiability of Causal Effects](https://mlsanity.com/paper/1302.4948/) (2013)
- [Avoiding Disparity Amplification under Different Worldviews](https://mlsanity.com/paper/1808.08619/) (2018)
- [Structure Learning of Linear Gaussian Structural Equation Models with Weak Edges](https://mlsanity.com/paper/1707.07560/) (2017)

## Built on by (most cited first, 6 of 6)

- [Unveiling and Causalizing CoT: A Causal Pespective](https://mlsanity.com/paper/2502.18239/) (2025)
- [What is Fair? Defining Fairness in Machine Learning for Health](https://mlsanity.com/paper/2406.09307/) (2024)
- [CausalPre: Scalable and Effective Data Pre-Processing for Causal Fairness](https://mlsanity.com/paper/2509.15199/) (2025)
- [Testing for Causal Fairness](https://mlsanity.com/paper/2502.12874/) (2025)
- [Fairness under Graph Uncertainty: Achieving Interventional Fairness with Partially Known Causal Graphs over Clusters of Variables](https://mlsanity.com/paper/2602.23611/) (2026)
- [Fair Data Pre-Processing with Imperfect Attribute Space](https://mlsanity.com/paper/2603.26456/) (2026)

## Abstract (arXiv)

Fair machine learning aims to prevent discrimination against individuals or sub-populations based on sensitive attributes such as gender and race. In recent years, causal inference methods have been increasingly used in fair machine learning to measure unfairness by causal effects. However, current methods assume that the true causal graph is given, which is often not true in real-world applications. To address this limitation, this paper proposes a framework for achieving causal fairness based on the notion of interventions when the true causal graph is partially known. The proposed approach involves modeling fair prediction using a Partially Directed Acyclic Graph (PDAG), specifically, a class of causal DAGs that can be learned from observational data combined with domain knowledge. The PDAG is used to measure causal fairness, and a constrained optimization problem is formulated to balance between fairness and accuracy. Results on both simulated and real-world datasets demonstrate the effectiveness of this method.