# Causal Fair Metric: Bridging Causality, Individual Fairness, and Adversarial Robustness

arXiv: https://arxiv.org/abs/2310.19391 · HTML: https://mlsanity.com/paper/2310.19391/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 42 references that are in the map.
- First posted on arXiv 30 Oct 2023.

## Builds on (most cited first, 22 of 22)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Avoiding Discrimination through Causal Reasoning](https://mlsanity.com/paper/1706.02744/) (2017)
- [Fair Inference On Outcomes](https://mlsanity.com/paper/1705.10378/) (2017)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [Training individually fair ML models with Sensitive Subspace Robustness](https://mlsanity.com/paper/1907.00020/) (2019)
- [Learning Certified Individually Fair Representations](https://mlsanity.com/paper/2002.10312/) (2020)
- [Online Learning with an Unknown Fairness Metric](https://mlsanity.com/paper/1802.06936/) (2018)
- [On the Adversarial Robustness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2112.11313/) (2021)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Two Simple Ways to Learn Individual Fairness Metrics from Data](https://mlsanity.com/paper/2006.11439/) (2020)
- [Metric Learning for Individual Fairness](https://mlsanity.com/paper/1906.00250/) (2019)
- [Verifying Individual Fairness in Machine Learning Models](https://mlsanity.com/paper/2006.11737/) (2020)
- [Metric-Free Individual Fairness in Online Learning](https://mlsanity.com/paper/2002.05474/) (2020)
- [Provably Fair Representations](https://mlsanity.com/paper/1710.04394/) (2017)
- [Optimal Decision Trees for Nonlinear Metrics](https://mlsanity.com/paper/2009.06921/) (2020)
- [Robustness Implies Fairness in Causal Algorithmic Recourse](https://mlsanity.com/paper/2302.03465/) (2023)
- [Spectral, Probabilistic, and Deep Metric Learning: Tutorial and Survey](https://mlsanity.com/paper/2201.09267/) (2022)
- [Causal Adversarial Perturbations for Individual Fairness and Robustness in Heterogeneous Data Spaces](https://mlsanity.com/paper/2308.08938/) (2023)
- [Distance Shrinkage and Euclidean Embedding via Regularized Kernel Estimation](https://mlsanity.com/paper/1409.5009/) (2014)

## Built on by (most cited first, 3 of 3)

- [Causality Is Key to Understand and Balance Multiple Goals in Trustworthy ML and Foundation Models](https://mlsanity.com/paper/2502.21123/) (2025)
- [Collective Counterfactual Explanations: Balancing Individual Goals and Collective Dynamics](https://mlsanity.com/paper/2402.04579/) (2024)
- [Wasserstein Distributionally Robust Optimization Through the Lens of Structural Causal Models and Individual Fairness](https://mlsanity.com/paper/2509.26275/) (2025)

## Abstract (arXiv)

Despite the essential need for comprehensive considerations in responsible AI, factors like robustness, fairness, and causality are often studied in isolation. Adversarial perturbation, used to identify vulnerabilities in models, and individual fairness, aiming for equitable treatment of similar individuals, despite initial differences, both depend on metrics to generate comparable input data instances. Previous attempts to define such joint metrics often lack general assumptions about data or structural causal models and were unable to reflect counterfactual proximity. To address this, our paper introduces a causal fair metric formulated based on causal structures encompassing sensitive attributes and protected causal perturbation. To enhance the practicality of our metric, we propose metric learning as a method for metric estimation and deployment in real-world problems in the absence of structural causal models. We also demonstrate the application of our novel metric in classifiers. Empirical evaluation of real-world and synthetic datasets illustrates the effectiveness of our proposed metric in achieving an accurate classifier with fairness, resilience to adversarial perturbations, and a nuanced understanding of causal relationships.