# Counterfactual explainability and analysis of variance

arXiv: https://arxiv.org/abs/2411.01625 · HTML: https://mlsanity.com/paper/2411.01625/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 74 references that are in the map.
- First posted on arXiv 3 Nov 2024.

## Builds on (most cited first, 13 of 13)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [The Shapley Taylor Interaction Index](https://mlsanity.com/paper/1902.05622/) (2019)
- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [A general framework for inference on algorithm-agnostic variable importance](https://mlsanity.com/paper/2004.03683/) (2020)
- [Principal Fairness for Human and Algorithmic Decision-Making](https://mlsanity.com/paper/2005.10400/) (2020)
- [Quantifying intrinsic causal contributions via structure preserving interventions](https://mlsanity.com/paper/2007.00714/) (2020)
- [Variable importance measures for heterogeneous treatment effects](https://mlsanity.com/paper/2204.06030/) (2022)
- [Bridging multiple worlds: multi-marginal optimal transport for causal partial-identification problem](https://mlsanity.com/paper/2406.07868/) (2024)

## Abstract (arXiv)

Existing tools for explaining complex models and systems are associational rather than causal and do not provide mechanistic understanding. We propose a new notion called counterfactual explainability for causal attribution that is motivated by the concept of genetic heritability in twin studies. Counterfactual explainability extends methods for global sensitivity analysis (including the functional analysis of variance and Sobol's indices), which assumes independent explanatory variables, to dependent explanations by using a directed acyclic graphs to describe their causal relationship. Therefore, this explanability measure directly incorporates causal mechanisms by construction. Under a comonotonicity assumption, we discuss methods for estimating counterfactual explainability and apply them to a real dataset dataset to explain income inequality by gender, race, and educational attainment.