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In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…

Artificial Intelligence · Computer Science 2014-05-26 Phil Maguire , Philippe Moser , Rebecca Maguire , Mark Keane

We introduce new inference procedures for counterfactual and synthetic control methods for policy evaluation. We recast the causal inference problem as a counterfactual prediction and a structural breaks testing problem. This allows us to…

Econometrics · Economics 2022-01-26 Victor Chernozhukov , Kaspar Wüthrich , Yinchu Zhu

We present a basis for studying questions of cause and effect in statistics which subsumes and reconciles the models proposed by Pearl, Robins, Rubin and others, and which, as far as mathematical notions and notation are concerned, is…

Statistics Theory · Mathematics 2023-04-18 José A. Ferreira

Probabilities of causation provide principled ways to assess causal relationships but face computational challenges due to partial identifiability and latent confounding. This paper introduces both algorithmic simplifications, significantly…

In observational studies, causal inference relies on several key identifying assumptions. One identifiability condition is the positivity assumption, which requires the probability of treatment be bounded away from 0 and 1. That is, for…

Methodology · Statistics 2022-02-21 Yaqian Zhu , Nandita Mitra , Jason Roy

Counterfactual reasoning allows us to explore hypothetical scenarios in order to explain the impacts of our decisions. However, addressing such inquires is impossible without establishing the appropriate mathematical framework. In this…

Machine Learning · Computer Science 2025-06-25 Kurt Butler , Marija Iloska , Petar M. Djuric

Counterfactual decision-making in the face of uncertainty involves selecting the optimal action from several alternatives using causal reasoning. Decision-makers often rank expected potential outcomes (or their corresponding utility and…

Artificial Intelligence · Computer Science 2025-11-17 Yuta Kawakami , Jin Tian

The DUCK-calculus presented here is a recent approach to cope with probabilistic uncertainty in a sound and efficient way. Uncertain rules with bounds for probabilities and explicit conditional independences can be maintained incrementally.…

Artificial Intelligence · Computer Science 2013-03-25 Helmut Thone , Ulrich Guntzer , Werner Kiessling

Counterfactual explanations (CEs) offer interpretable insights into machine learning predictions by answering ``what if?" questions. However, in real-world settings where models are frequently updated, existing counterfactual explanations…

Machine Learning · Computer Science 2026-02-12 Jamie Duell , Xiuyi Fan

We show that one can perform causal inference in a natural way for continuous-time scenarios using tools from stochastic analysis. This provides new alternatives to the positivity condition for inverse probability weighting. The probability…

Statistics Theory · Mathematics 2013-04-23 Kjetil Røysland

Current pre-trained language models have enabled remarkable improvements in downstream tasks, but it remains difficult to distinguish effects of statistical correlation from more systematic logical reasoning grounded on the understanding of…

Computation and Language · Computer Science 2023-05-29 Jiaxuan Li , Lang Yu , Allyson Ettinger

We discuss the problem of bounding partially identifiable queries, such as counterfactuals, in Pearlian structural causal models. A recently proposed iterated EM scheme yields an inner approximation of those bounds by sampling the…

Artificial Intelligence · Computer Science 2023-10-06 David Huber , Yizuo Chen , Alessandro Antonucci , Adnan Darwiche , Marco Zaffalon

We provide an optimization-based framework to perform counterfactual analysis in a dynamic model with hidden states. Our framework is grounded in the ``abduction, action, and prediction'' approach to answer counterfactual queries and…

Machine Learning · Computer Science 2023-05-09 Martin Haugh , Raghav Singal

Machine-learning models are increasingly driving decisions in high-stakes settings, such as finance, law, and hiring, thus, highlighting the need for transparency. However, the key challenge is to balance transparency -- clarifying `why' a…

Artificial Intelligence · Computer Science 2025-08-29 Sopam Dasgupta , Sadaf MD Halim , Joaquín Arias , Elmer Salazar , Gopal Gupta

Decision-making under uncertainty and causal thinking are fundamental aspects of intelligent reasoning. Decision-making has been well studied when the available information is considered at the associative (probabilistic) level. The…

Artificial Intelligence · Computer Science 2026-04-30 Mauricio Gonzalez Soto , David Danks , Hugo J. Escalante Balderas , L. Enrique Sucar

Explainable recommendation through counterfactual reasoning seeks to identify the influential aspects of items in recommendations, which can then be used as explanations. However, state-of-the-art approaches, which aim to minimize changes…

Information Retrieval · Computer Science 2025-10-14 Yi Yu , Zhenxing Hu

We propose a new definition of actual causes, using structural equations to model counterfactuals.We show that the definitions yield a plausible and elegant account ofcausation that handles well examples which have caused problems forother…

Artificial Intelligence · Computer Science 2013-01-14 Joseph Y. Halpern , Judea Pearl

AI-driven outcomes can be challenging for end-users to understand. Explanations can address two key questions: "Why this outcome?" (factual) and "Why not another?" (counterfactual). While substantial efforts have been made to formalize…

Artificial Intelligence · Computer Science 2025-03-21 Suryani Lim , Henri Prade , Gilles Richard

Causal approaches to fairness have seen substantial recent interest, both from the machine learning community and from wider parties interested in ethical prediction algorithms. In no small part, this has been due to the fact that causal…

Machine Learning · Computer Science 2019-08-17 Niki Kilbertus , Philip J. Ball , Matt J. Kusner , Adrian Weller , Ricardo Silva

Lewis' theory of counterfactuals is the foundation of many contemporary notions of causality. In this paper, we extend this theory in the temporal direction to enable symbolic counterfactual reasoning on infinite sequences, such as…

Logic in Computer Science · Computer Science 2023-06-16 Bernd Finkbeiner , Julian Siber