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Counterfactual reasoning is pivotal in human cognition and especially important for providing explanations and making decisions. While Judea Pearl's influential approach is theoretically elegant, its generation of a counterfactual scenario…

Artificial Intelligence · Computer Science 2024-11-01 Guang-Yuan Hao , Jiji Zhang , Biwei Huang , Hao Wang , Kun Zhang

Counterfactuals and counterfactual reasoning underpin numerous techniques for auditing and understanding artificial intelligence (AI) systems. The traditional paradigm for counterfactual reasoning in this literature is the interventional…

Artificial Intelligence · Computer Science 2024-01-26 Lucius E. J. Bynum , Joshua R. Loftus , Julia Stoyanovich

Counterfactual reasoning, a cornerstone of human cognition and decision-making, is often seen as the 'holy grail' of causal learning, with applications ranging from interpreting machine learning models to promoting algorithmic fairness.…

Machine Learning · Computer Science 2025-04-11 Yahya Aalaila , Gerrit Großmann , Sumantrak Mukherjee , Jonas Wahl , Sebastian Vollmer

As machine learning is increasingly used to inform consequential decision-making (e.g., pre-trial bail and loan approval), it becomes important to explain how the system arrived at its decision, and also suggest actions to achieve a…

Machine Learning · Computer Science 2020-10-09 Amir-Hossein Karimi , Bernhard Schölkopf , Isabel Valera

We introduce an approach to counterfactual inference based on merging information from multiple datasets. We consider a causal reformulation of the statistical marginal problem: given a collection of marginal structural causal models (SCMs)…

Artificial Intelligence · Computer Science 2022-07-18 Luigi Gresele , Julius von Kügelgen , Jonas M. Kübler , Elke Kirschbaum , Bernhard Schölkopf , Dominik Janzing

We mathematically axiomatise the stochastics of counterfactuals, by introducing two related frameworks, called counterfactual probability spaces and counterfactual causal spaces, which we collectively term counterfactual spaces. They are,…

Statistics Theory · Mathematics 2026-01-05 Junhyung Park , Fanny Yang , Thomas Icard

Evaluating hypothetical statements about how the world would be had a different course of action been taken is arguably one key capability expected from modern AI systems. Counterfactual reasoning underpins discussions in fairness, the…

Machine Learning · Computer Science 2022-10-04 Kevin Xia , Yushu Pan , Elias Bareinboim

Counterfactual thinking is a crucial yet challenging topic for artificial intelligence to learn knowledge from data and ultimately improve performance for new scenarios. Many research works, including the Potential Outcome Model (POM) and…

Artificial Intelligence · Computer Science 2026-02-24 Mingyu Kang , Duxin Chen , Ziyuan Pu , Jianxi Gao , Wenwu Yu

Counterfactual explanations are emerging as an attractive option for providing recourse to individuals adversely impacted by algorithmic decisions. As they are deployed in critical applications (e.g. law enforcement, financial lending), it…

Machine Learning · Computer Science 2021-11-05 Dylan Slack , Sophie Hilgard , Himabindu Lakkaraju , Sameer Singh

Counterfactual reasoning aims at answering contrary-to-fact questions like ``Would have Alice recovered had she taken aspirin?'' and corresponds to the most fine-grained layer of causation. Critically, while many counterfactual statements…

Artificial Intelligence · Computer Science 2025-09-23 Lucas de Lara

Counterfactuals are often described as 'retrospective,' focusing on hypothetical alternatives to a realized past. This description relates to an often implicit assumption about the structure and stability of exogenous variables in the…

Artificial Intelligence · Computer Science 2022-12-09 Lucius E. J. Bynum , Joshua R. Loftus , Julia Stoyanovich

Counterfactuals answer questions of what would have been observed under altered circumstances and can therefore offer valuable insights. Whereas the classical interventional interpretation of counterfactuals has been studied extensively,…

Artificial Intelligence · Computer Science 2024-08-13 Klaus-Rudolf Kladny , Julius von Kügelgen , Bernhard Schölkopf , Michael Muehlebach

Counterfactual explanations (CEs) are methods for generating an alternative scenario that produces a different desirable outcome. For example, if a student is predicted to fail a course, then counterfactual explanations can provide the…

Machine Learning · Statistics 2023-01-09 Bevan I. Smith

Counterfactual frameworks have grown popular in machine learning for both explaining algorithmic decisions but also defining individual notions of fairness, more intuitive than typical group fairness conditions. However, state-of-the-art…

Artificial Intelligence · Computer Science 2023-01-09 Lucas de Lara , Alberto González-Sanz , Nicholas Asher , Laurent Risser , Jean-Michel Loubes

Machine learning plays a role in many deployed decision systems, often in ways that are difficult or impossible to understand by human stakeholders. Explaining, in a human-understandable way, the relationship between the input and output of…

Machine Learning · Computer Science 2022-11-17 Sahil Verma , Varich Boonsanong , Minh Hoang , Keegan E. Hines , John P. Dickerson , Chirag Shah

Most counterfactual inference frameworks traditionally assume acyclic structural causal models (SCMs), i.e. directed acyclic graphs (DAGs). However, many real-world systems (e.g. biological systems) contain feedback loops or cyclic…

Artificial Intelligence · Computer Science 2026-01-21 Saptarshi Saha , Dhruv Vansraj Rathore , Utpal Garain

Structural causal models are the basic modelling unit in Pearl's causal theory; in principle they allow us to solve counterfactuals, which are at the top rung of the ladder of causation. But they often contain latent variables that limit…

Artificial Intelligence · Computer Science 2021-11-23 Marco Zaffalon , Alessandro Antonucci , Rafael Cabañas

Counterfactual inference considers a hypothetical intervention in a parallel world that shares some evidence with the factual world. If the evidence specifies a conditional distribution on a manifold, counterfactuals may be analytically…

Machine Learning · Statistics 2024-07-03 Juha Karvanen , Santtu Tikka , Matti Vihola

Counterfactual fairness alleviates the discrimination between the model prediction toward an individual in the actual world (observational data) and that in counterfactual world (i.e., what if the individual belongs to other sensitive…

Machine Learning · Computer Science 2023-03-28 Tri Dung Duong , Qian Li , Guandong Xu

Counterfactual explanations have emerged as a prominent method in Explainable Artificial Intelligence (XAI), providing intuitive and actionable insights into Machine Learning model decisions. In contrast to other traditional feature…

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