# Results on Counterfactual Invariance

arXiv: https://arxiv.org/abs/2307.08519 · HTML: https://mlsanity.com/paper/2307.08519/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 18 references that are in the map.
- First posted on arXiv 17 Jul 2023.

## Builds on (most cited first, 10 of 10)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions](https://mlsanity.com/paper/1707.06422/) (2017)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Counterfactual Invariance to Spurious Correlations: Why and How to Pass Stress Tests](https://mlsanity.com/paper/2106.00545/) (2021)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Strong Completeness and Faithfulness in Bayesian Networks](https://mlsanity.com/paper/1302.4973/) (2013)
- [Causal Inference Through the Structural Causal Marginal Problem](https://mlsanity.com/paper/2202.01300/) (2022)
- [Selection, Ignorability and Challenges With Causal Fairness](https://mlsanity.com/paper/2202.13774/) (2022)
- [Learning Counterfactually Invariant Predictors](https://mlsanity.com/paper/2207.09768/) (2022)

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

- [The Fragility of Fairness: Causal Sensitivity Analysis for Fair Machine Learning](https://mlsanity.com/paper/2410.09600/) (2024)
- [Test-Time Fairness and Robustness in Large Language Models](https://mlsanity.com/paper/2406.07685/) (2024)
- [AI Alignment in Medical Imaging: Unveiling Hidden Biases Through Counterfactual Analysis](https://mlsanity.com/paper/2504.19621/) (2025)
- [MELD: Multi-Task Equilibrated Learning Detector for AI-Generated Text](https://mlsanity.com/paper/2605.06903/) (2026)

## Abstract (arXiv)

In this paper we provide a theoretical analysis of counterfactual invariance. We present a variety of existing definitions, study how they relate to each other and what their graphical implications are. We then turn to the current major question surrounding counterfactual invariance, how does it relate to conditional independence? We show that whilst counterfactual invariance implies conditional independence, conditional independence does not give any implications about the degree or likelihood of satisfying counterfactual invariance. Furthermore, we show that for discrete causal models counterfactually invariant functions are often constrained to be functions of particular variables, or even constant.