# Sequential Conditional Transport on Probabilistic Graphs for Interpretable Counterfactual Fairness

arXiv: https://arxiv.org/abs/2408.03425 · HTML: https://mlsanity.com/paper/2408.03425/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 71 references that are in the map.
- First posted on arXiv 6 Aug 2024.

## Builds on (most cited first, 21 of 21)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [Avoiding Discrimination through Causal Reasoning](https://mlsanity.com/paper/1706.02744/) (2017)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Supervised Training of Conditional Monge Maps](https://mlsanity.com/paper/2206.14262/) (2022)
- [FlipTest: Fairness Testing via Optimal Transport](https://mlsanity.com/paper/1906.09218/) (2019)
- [Local Explanations via Necessity and Sufficiency: Unifying Theory and Practice](https://mlsanity.com/paper/2103.14651/) (2021)
- [Active Bayesian Causal Inference](https://mlsanity.com/paper/2206.02063/) (2022)
- [Fair Data Adaptation with Quantile Preservation](https://mlsanity.com/paper/1911.06685/) (2019)
- [Transport-based Counterfactual Models](https://mlsanity.com/paper/2108.13025/) (2021)
- [Conditional Optimal Transport on Function Spaces](https://mlsanity.com/paper/2311.05672/) (2023)
- [Causal transport in discrete time and applications](https://mlsanity.com/paper/1606.04062/) (2016)
- [fairadapt: Causal Reasoning for Fair Data Pre-processing](https://mlsanity.com/paper/2110.10200/) (2021)
- [On Learning Necessary and Sufficient Causal Graphs](https://mlsanity.com/paper/2301.12389/) (2023)
- [Learning for Counterfactual Fairness from Observational Data](https://mlsanity.com/paper/2307.08232/) (2023)
- [Multivariate Counterfactual Systems And Causal Graphical Models](https://mlsanity.com/paper/2008.06017/) (2020)
- [Optimal transport and Wasserstein distances for causal models](https://mlsanity.com/paper/2303.14085/) (2023)
- [FairPFN: Transformers Can do Counterfactual Fairness](https://mlsanity.com/paper/2407.05732/) (2024)

## Built on by (most cited first, 4 of 4)

- [Lookahead Counterfactual Fairness](https://mlsanity.com/paper/2412.01065/) (2024)
- [Optimal Transport on Categorical Data for Counterfactuals using Compositional Data and Dirichlet Transport](https://mlsanity.com/paper/2501.15549/) (2025)
- [What is a good matching of probability measures? A counterfactual lens on transport maps](https://mlsanity.com/paper/2509.16027/) (2025)
- [A Bayesian Approach to Membership Inference for Statistical Release](https://mlsanity.com/paper/2605.30203/) (2026)

## Abstract (arXiv)

In this paper, we link two existing approaches to derive counterfactuals: adaptations based on a causal graph, and optimal transport. We extend "Knothe's rearrangement" and "triangular transport" to probabilistic graphical models, and use this counterfactual approach, referred to as sequential transport, to discuss fairness at the individual level. After establishing the theoretical foundations of the proposed method, we demonstrate its application through numerical experiments on both synthetic and real datasets.