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We consider identification and inference about a counterfactual outcome mean when there is unmeasured confounding using tools from proximal causal inference (Miao et al. [2018], Tchetgen Tchetgen et al. [2020]). Proximal causal inference…

Methodology · Statistics 2023-10-03 Jeffrey Zhang , Wei Li , Wang Miao , Eric Tchetgen Tchetgen

We consider learning the possible causal direction of two observed variables in the presence of latent confounding variables. Several existing methods have been shown to consistently estimate causal direction assuming linear or some type of…

Machine Learning · Statistics 2014-05-21 Shohei Shimizu , Kenneth Bollen

In this paper, the relationship between probabilistic graphical models, in particular Bayesian networks, and causal diagrams, also called structural causal models, is studied. Structural causal models are deterministic models, based on…

Artificial Intelligence · Computer Science 2026-04-24 Peter J. F. Lucas , Eleonora Zullo , Fabio Stella

To construct interpretable explanations that are consistent with the original ML model, counterfactual examples---showing how the model's output changes with small perturbations to the input---have been proposed. This paper extends the work…

Machine Learning · Computer Science 2020-06-16 Divyat Mahajan , Chenhao Tan , Amit Sharma

With the increasing impact of algorithmic decision-making on human lives, the interpretability of models has become a critical issue in machine learning. Counterfactual explanation is an important method in the field of interpretable…

Machine Learning · Computer Science 2024-07-17 Ao Xu , Tieru Wu

Predictive models are being increasingly used to support consequential decision making at the individual level in contexts such as pretrial bail and loan approval. As a result, there is increasing social and legal pressure to provide…

Machine Learning · Computer Science 2020-03-02 Amir-Hossein Karimi , Gilles Barthe , Borja Balle , Isabel Valera

This tutorial provides a concise introduction to modern causal modeling by integrating potential outcomes and graphical methods. We motivate causal questions such as counterfactual reasoning under interventions and define binary treatments…

Methodology · Statistics 2025-06-27 Gauranga Kumar Baishya

This paper is directed towards combining Pearl's structural-model approach to causal reasoning with high-level formalisms for reasoning about actions. More precisely, we present a combination of Pearl's structural-model approach with…

Artificial Intelligence · Computer Science 2012-12-12 Alberto Finzi , Thomas Lukasiewicz

A definition of causality introduced by Halpern and Pearl, which uses structural equations, is reviewed. A more refined definition is then considered, which takes into account issues of normality and typicality, which are well known to…

Artificial Intelligence · Computer Science 2014-12-10 Joseph Y. Halpern

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

We present a general causal generative modelling framework for accurate estimation of high fidelity image counterfactuals with deep structural causal models. Estimation of interventional and counterfactual queries for high-dimensional…

Machine Learning · Computer Science 2023-07-19 Fabio De Sousa Ribeiro , Tian Xia , Miguel Monteiro , Nick Pawlowski , Ben Glocker

Causal world models are systems that can answer counterfactual questions about an environment of interest, i.e. predict how it would have evolved if an arbitrary subset of events had been realized differently. It requires understanding the…

Artificial Intelligence · Computer Science 2025-05-21 Gaël Gendron , Jože M. Rožanec , Michael Witbrock , Gillian Dobbie

Physical and optical factors interacting with sensor characteristics create complex image degradation patterns. Despite advances in deep learning-based super-resolution, existing methods overlook the causal nature of degradation by adopting…

Computer Vision and Pattern Recognition · Computer Science 2025-01-28 Zhengyang Lu , Bingjie Lu , Feng Wang

Causal models have proven extremely useful in offering formal representations of causal relationships between a set of variables. Yet in many situations, there are non-causal relationships among variables. For example, we may want variables…

Artificial Intelligence · Computer Science 2023-01-18 Sander Beckers , Joseph Y. Halpern , Christopher Hitchcock

This paper clarifies how and why structural demand models (Berry and Haile, 2014, 2024) predict unit-level counterfactual outcomes. We do so by casting structural assumptions equivalently as restrictions on the joint distribution of…

Econometrics · Economics 2025-11-07 Jiafeng Chen

Counterfactual explanations and adversarial attacks have a related goal: flipping output labels with minimal perturbations regardless of their characteristics. Yet, adversarial attacks cannot be used directly in a counterfactual explanation…

Computer Vision and Pattern Recognition · Computer Science 2023-03-20 Guillaume Jeanneret , Loïc Simon , Frédéric Jurie

The notion of a non-deterministic logical matrix (where connectives are interpreted as multi-functions) extends the traditional semantics for propositional logics based on logical matrices (where connectives are interpreted as functions).…

Logic · Mathematics 2024-12-19 Carlos Caleiro , Pedro Filipe , Sérgio Marcelino

Learning the causal structure that underlies data is a crucial step towards robust real-world decision making. The majority of existing work in causal inference focuses on determining a single directed acyclic graph (DAG) or a Markov…

Machine Learning · Computer Science 2021-06-15 Yashas Annadani , Jonas Rothfuss , Alexandre Lacoste , Nino Scherrer , Anirudh Goyal , Yoshua Bengio , Stefan Bauer

We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…

Logic in Computer Science · Computer Science 2021-06-03 Duligur Ibeling , Thomas Icard

We propose a framework for analyzing the sensitivity of counterfactuals to parametric assumptions about the distribution of latent variables in structural models. In particular, we derive bounds on counterfactuals as the distribution of…

Econometrics · Economics 2024-03-26 Timothy Christensen , Benjamin Connault