# Backtracking Counterfactuals

arXiv: https://arxiv.org/abs/2211.00472 · HTML: https://mlsanity.com/paper/2211.00472/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 49 references that are in the map.
- First posted on arXiv 1 Nov 2022.

## Builds on (most cited first, 18 of 18)

- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [The What-If Tool: Interactive Probing of Machine Learning Models](https://mlsanity.com/paper/1907.04135/) (2019)
- [Avoiding Discrimination through Causal Reasoning](https://mlsanity.com/paper/1706.02744/) (2017)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [Towards Realistic Individual Recourse and Actionable Explanations in Black-Box Decision Making Systems](https://mlsanity.com/paper/1907.09615/) (2019)
- [On the Fairness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2010.06529/) (2020)
- [Causal structure based root cause analysis of outliers](https://mlsanity.com/paper/1912.02724/) (2019)
- [Causal Fairness Analysis](https://mlsanity.com/paper/2207.11385/) (2022)
- [From Statistical to Causal Learning](https://mlsanity.com/paper/2204.00607/) (2022)
- [What's Sex Got To Do With Fair Machine Learning?](https://mlsanity.com/paper/2006.01770/) (2020)
- [Causal Explanations and XAI](https://mlsanity.com/paper/2201.13169/) (2022)
- [Counterfactual Explanations as Interventions in Latent Space](https://mlsanity.com/paper/2106.07754/) (2021)
- [Quantifying intrinsic causal contributions via structure preserving interventions](https://mlsanity.com/paper/2007.00714/) (2020)

## Built on by (most cited first, 16 of 16)

- [Causal normalizing flows: from theory to practice](https://mlsanity.com/paper/2306.05415/) (2023)
- [Benchmarking Counterfactual Image Generation](https://mlsanity.com/paper/2403.20287/) (2024)
- [Root Cause Analysis of Outliers with Missing Structural Knowledge](https://mlsanity.com/paper/2406.05014/) (2024)
- [Targeted Reduction of Causal Models](https://mlsanity.com/paper/2311.18639/) (2023)
- [Deep Backtracking Counterfactuals for Causally Compliant Explanations](https://mlsanity.com/paper/2310.07665/) (2023)
- [A Measure-Theoretic Axiomatisation of Causality](https://mlsanity.com/paper/2305.17139/) (2023)
- [Counterfactual Formulation of Patient-Specific Root Causes of Disease](https://mlsanity.com/paper/2305.17574/) (2023)
- [Root Cause Analysis of Outliers in Unknown Cyclic Graphs](https://mlsanity.com/paper/2510.06995/) (2025)
- [Toward Universal Laws of Outlier Propagation](https://mlsanity.com/paper/2502.08593/) (2025)
- [Beyond Single-Feature Importance with ICECREAM](https://mlsanity.com/paper/2307.09779/) (2023)
- [Algorithmic Recourse in Abnormal Multivariate Time Series](https://mlsanity.com/paper/2309.16896/) (2023)
- [Natural Counterfactuals With Necessary Backtracking](https://mlsanity.com/paper/2402.01607/) (2024)
- [On Measuring Intrinsic Causal Attributions in Deep Neural Networks](https://mlsanity.com/paper/2505.09660/) (2025)
- [Cyclic Counterfactuals under Shift-Scale Interventions](https://mlsanity.com/paper/2510.25005/) (2025)
- [Causality Without Causal Models](https://mlsanity.com/paper/2511.21260/) (2025)
- [CoBe: A Benchmark For Conversational Counterfactual Text Editing](https://mlsanity.com/paper/2610.13057/) (2026)

## Abstract (arXiv)

Counterfactual reasoning -- envisioning hypothetical scenarios, or possible worlds, where some circumstances are different from what (f)actually occurred (counter-to-fact) -- is ubiquitous in human cognition. Conventionally, counterfactually-altered circumstances have been treated as "small miracles" that locally violate the laws of nature while sharing the same initial conditions. In Pearl's structural causal model (SCM) framework this is made mathematically rigorous via interventions that modify the causal laws while the values of exogenous variables are shared. In recent years, however, this purely interventionist account of counterfactuals has increasingly come under scrutiny from both philosophers and psychologists. Instead, they suggest a backtracking account of counterfactuals, according to which the causal laws remain unchanged in the counterfactual world; differences to the factual world are instead "backtracked" to altered initial conditions (exogenous variables). In the present work, we explore and formalise this alternative mode of counterfactual reasoning within the SCM framework. Despite ample evidence that humans backtrack, the present work constitutes, to the best of our knowledge, the first general account and algorithmisation of backtracking counterfactuals. We discuss our backtracking semantics in the context of related literature and draw connections to recent developments in explainable artificial intelligence (XAI).