# Counterfactual Fairness with Partially Known Causal Graph

arXiv: https://arxiv.org/abs/2205.13972 · HTML: https://mlsanity.com/paper/2205.13972/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 86 references that are in the map.
- First posted on arXiv 27 May 2022.

## Builds on (most cited first, 26 of 26)

- [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)
- [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)
- [Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles](https://mlsanity.com/paper/2005.00610/) (2020)
- [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)
- [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)
- [Selection, Ignorability and Challenges With Causal Fairness](https://mlsanity.com/paper/2202.13774/) (2022)
- [Minimal enumeration of all possible total effects in a Markov equivalence class](https://mlsanity.com/paper/2010.08611/) (2020)
- [A Local Method for Identifying Causal Relations under Markov Equivalence](https://mlsanity.com/paper/2102.12685/) (2021)
- [Avoiding Disparity Amplification under Different Worldviews](https://mlsanity.com/paper/1808.08619/) (2018)
- [Definite Non-Ancestral Relations and Structure Learning](https://mlsanity.com/paper/2105.10350/) (2021)

## Built on by (most cited first, 20 of 20)

- [Causal Context Connects Counterfactual Fairness to Robust Prediction and Group Fairness](https://mlsanity.com/paper/2310.19691/) (2023)
- [Learning for Counterfactual Fairness from Observational Data](https://mlsanity.com/paper/2307.08232/) (2023)
- [Chasing Fairness Under Distribution Shift: A Model Weight Perturbation Approach](https://mlsanity.com/paper/2303.03300/) (2023)
- [Interventional Fairness on Partially Known Causal Graphs: A Constrained Optimization Approach](https://mlsanity.com/paper/2401.10632/) (2024)
- [Local Causal Discovery with Background Knowledge](https://mlsanity.com/paper/2408.07890/) (2024)
- [Counterfactually Fair Reinforcement Learning via Sequential Data Preprocessing](https://mlsanity.com/paper/2501.06366/) (2025)
- [Fairness-Driven LLM-based Causal Discovery with Active Learning and Dynamic Scoring](https://mlsanity.com/paper/2503.17569/) (2025)
- [Retiring DeltaDP: New Distribution-Level Metrics for Demographic Parity](https://mlsanity.com/paper/2301.13443/) (2023)
- [A Theoretical Approach to Characterize the Accuracy-Fairness Trade-off Pareto Frontier](https://mlsanity.com/paper/2310.12785/) (2023)
- [Causal Feature Selection for Responsible Machine Learning](https://mlsanity.com/paper/2402.02696/) (2024)
- [Lookahead Counterfactual Fairness](https://mlsanity.com/paper/2412.01065/) (2024)
- [Causality Is Key to Understand and Balance Multiple Goals in Trustworthy ML and Foundation Models](https://mlsanity.com/paper/2502.21123/) (2025)
- [A Note on Bias to Complete](https://mlsanity.com/paper/2402.11710/) (2024)
- [Counterfactual Fairness with Graph Uncertainty](https://mlsanity.com/paper/2601.03203/) (2026)
- [Trustworthy AI Suffers from Invariance Conflicts and Causality is The Solution](https://mlsanity.com/paper/2605.02640/) (2026)
- [Learning Counterfactually Fair Models via Improved Generation with Neural Causal Models](https://mlsanity.com/paper/2502.12796/) (2025)
- [Testing for Causal Fairness](https://mlsanity.com/paper/2502.12874/) (2025)
- [Position: Beyond Sensitive Attributes, ML Fairness Should Quantify Structural Injustice via Social Determinants](https://mlsanity.com/paper/2508.08337/) (2025)
- [Causal Sensitivity Identification using Generative Learning](https://mlsanity.com/paper/2509.01352/) (2025)
- [A Distribution Mapping Approach to Counterfactually Fair Reinforcement Learning](https://mlsanity.com/paper/2608.08743/) (2026)

## Abstract (arXiv)

Fair machine learning aims to avoid treating individuals or sub-populations unfavourably based on textitsensitive attributes, such as gender and race. Those methods in fair machine learning that are built on causal inference ascertain discrimination and bias through causal effects. Though causality-based fair learning is attracting increasing attention, current methods assume the true causal graph is fully known. This paper proposes a general method to achieve the notion of counterfactual fairness when the true causal graph is unknown. To be able to select features that lead to counterfactual fairness, we derive the conditions and algorithms to identify ancestral relations between variables on a textitPartially Directed Acyclic Graph (PDAG), specifically, a class of causal DAGs that can be learned from observational data combined with domain knowledge. Interestingly, we find that counterfactual fairness can be achieved as if the true causal graph were fully known, when specific background knowledge is provided: the sensitive attributes do not have ancestors in the causal graph. Results on both simulated and real-world datasets demonstrate the effectiveness of our method.