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Causal modelling frameworks link observable correlations to causal explanations, which is a crucial aspect of science. These models represent causal relationships through directed graphs, with vertices and edges denoting systems and…

Quantum Physics · Physics 2025-02-10 Carla Ferradini , Victor Gitton , V. Vilasini

Causal opacity denotes the difficulty in understanding the "hidden" causal structure underlying the decisions of deep neural network (DNN) models. This leads to the inability to rely on and verify state-of-the-art DNN-based systems,…

The Rubin Causal Model (RCM) is a framework that allows to define the causal effect of an intervention as a contrast of potential outcomes. In recent years, several methods have been developed under the RCM to estimate causal effects in…

Econometrics · Economics 2021-09-02 Fiammetta Menchetti , Fabrizio Cipollini , Fabrizia Mealli

Recently, Bj{\o}ru et al. proposed a novel divide-and-conquer algorithm for bounding counterfactual probabilities in structural causal models (SCMs). They assumed that the SCMs were learned from purely observational data, leading to an…

Artificial Intelligence · Computer Science 2025-11-19 Anna Rodum Bjøru , Rafael Cabañas , Helge Langseth , Antonio Salmerón

Causal generative models provide a principled framework for answering observational, interventional, and counterfactual queries from observational data. However, many deep causal models rely on highly expressive architectures with opaque…

Machine Learning · Computer Science 2026-03-23 Alejandro Almodóvar , Mar Elizo , Patricia A. Apellániz , Santiago Zazo , Juan Parras

Structural-equations models (SEMs) are perhaps the most commonly used framework for modeling causality. However, as we show, naively extending this framework to infinitely many variables, which is necessary, for example, to model dynamical…

Artificial Intelligence · Computer Science 2021-12-20 Spencer Peters , Joseph Y. Halpern

The variability of structure in a finite Markov equivalence class of causally sufficient models represented by directed acyclic graphs has been fully characterized. Without causal sufficiency, an infinite semi-Markov equivalence class of…

Artificial Intelligence · Computer Science 2013-02-01 Benoit Desjardins

An introduction to the emerging fusion of machine learning and causal inference. The book presents ideas from classical structural equation models (SEMs) and their modern AI equivalent, directed acyclical graphs (DAGs) and structural causal…

It is known that the classical framework of causal models is not general enough to allow for causal reasoning about quantum systems. While the framework has been generalized in a variety of different ways to the quantum case, much of this…

Quantum Physics · Physics 2020-11-23 Jonathan Barrett , Robin Lorenz , Ognyan Oreshkov

Causal artificial intelligence aims to enhance explainability, trustworthiness, and robustness in AI by leveraging structural causal models (SCMs). In this pursuit, recent advances formalize network sheaves and cosheaves of causal…

Machine Learning · Computer Science 2026-02-04 Gabriele D'Acunto , Paolo Di Lorenzo , Sergio Barbarossa

Causal abstractions allow us to relate causal models on different levels of granularity. To ensure that the models agree on cause and effect, frameworks for causal abstractions define notions of consistency. Two distinct methods for causal…

Artificial Intelligence · Computer Science 2025-03-17 Willem Schooltink , Fabio Massimo Zennaro

We show that it is possible to understand and identify a decision maker's subjective causal judgements by observing her preferences over interventions. Following Pearl [2000], we represent causality using causal models (also called…

Theoretical Economics · Economics 2024-01-23 Joseph Y. Halpern , Evan Piermont

We extend two kinds of causal models, structural equation models and simulation models, to infinite variable spaces. This enables a semantics for conditionals founded on a calculus of intervention, and axiomatization of causal reasoning for…

Artificial Intelligence · Computer Science 2021-06-03 Duligur Ibeling , Thomas Icard

Large Language Models (LLMs) have recently shown great promise in planning and reasoning applications. These tasks demand robust systems, which arguably require a causal understanding of the environment. While LLMs can acquire and reflect…

Artificial Intelligence · Computer Science 2024-10-29 John Gkountouras , Matthias Lindemann , Phillip Lippe , Efstratios Gavves , Ivan Titov

Structural causal models postulate noisy functional relations among a set of interacting variables. The causal structure underlying each such model is naturally represented by a directed graph whose edges indicate for each variable which…

Statistics Theory · Mathematics 2022-03-15 David Strieder , Tobias Freidling , Stefan Haffner , Mathias Drton

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

Reward Models (RMs) are key components for evaluating and guiding language model outputs. However, traditional scalar RMs often struggle with incorporating contextual and background information during inference, leading to incomplete…

Artificial Intelligence · Computer Science 2025-10-07 Xiaoyu Liu , Di Liang , Chang Dai , Hongyu Shan , Peiyang Liu , Yonghao Liu , Muling Wu , Yuntao Li , Xianjie Wu , LI Miao , Jiangrong Shen , Minlong Peng

The aim of this paper is to discuss a recent result which shows that probabilistic inference in the presence of (unknown) causal mechanisms can be tractable for models that have traditionally been viewed as intractable. This result was…

Artificial Intelligence · Computer Science 2022-02-08 Adnan Darwiche

Causal models, also known as Structural Equation Models (SEM), are a well-known formalism for representing and reasoning about causal dependencies between events. In this paper, we show that Temporal SEMs (TSEMs), which extend SEMs to…

Formal Languages and Automata Theory · Computer Science 2026-05-08 Maksim Gladyshev , Natasha Alechina , Brian Logan

The aim of this paper is to offer the first systematic exploration and definition of equivalent causal models in the context where both models are not made up of the same variables. The idea is that two models are equivalent when they agree…

Artificial Intelligence · Computer Science 2020-12-11 Sander Beckers
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