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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

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 is a useful tool for comparing outcomes of interventions on complex systems. It requires us to represent the system in form of a structural causal model, complete with a causal diagram, probabilistic assumptions on…

Bayesian networks can be used to extract explanations about the observed state of a subset of variables. In this paper, we explicate the desiderata of an explanation and confront them with the concept of explanation proposed by existing…

Artificial Intelligence · Computer Science 2012-06-18 Ulf Nielsen , Jean-Philippe Pellet , André Elisseeff

Biological networks are a very convenient modelling and visualisation tool to discover knowledge from modern high-throughput genomics and postgenomics data sets. Indeed, biological entities are not isolated, but are components of complex…

Quantitative Methods · Quantitative Biology 2018-05-07 Alex White , Matthieu Vignes

Counterfactual explanations study what should have changed in order to get an alternative result, enabling end-users to understand machine learning mechanisms with counterexamples. Actionability is defined as the ability to transform the…

Artificial Intelligence · Computer Science 2025-08-05 Enrique Valero-Leal , Pedro Larrañaga , Concha Bielza

Causal Bayesian networks are 'causal' models since they make predictions about interventional distributions. To connect such causal model predictions to real-world outcomes, we must determine which actions in the world correspond to which…

Machine Learning · Statistics 2025-02-04 Frederik Hytting Jørgensen , Luigi Gresele , Sebastian Weichwald

Causal reasoning is essential for understanding decision-making about the behaviour of complex `ecosystems' of systems that underpin modern society, with security -- including issues around correctness, safety, resilience, etc. -- typically…

Logic in Computer Science · Computer Science 2025-08-05 Pinaki Chakraborty , Tristan Caulfield , David Pym

Ensuring safe operation of safety-critical complex systems interacting with their environment poses significant challenges, particularly when the system's world model relies on machine learning algorithms to process the perception input. A…

Robotics · Computer Science 2025-05-27 Roman Gansch , Lina Putze , Tjark Koopmann , Jan Reich , Christian Neurohr

Research in Cognitive Science suggests that humans understand and represent knowledge of the world through causal relationships. In addition to observations, they can rely on experimenting and counterfactual reasoning -- i.e. referring to…

Artificial Intelligence · Computer Science 2021-05-24 Kanvaly Fadiga , Etienne Houzé , Ada Diaconescu , Jean-Louis Dessalles

There is a brief description of the probabilistic causal graph model for representing, reasoning with, and learning causal structure using Bayesian networks. It is then argued that this model is closely related to how humans reason with and…

Artificial Intelligence · Computer Science 2013-02-08 Scott B. Morris , Doug Cork , Richard E. Neapolitan

In this dissertation we develop a new formal graphical framework for causal reasoning. Starting with a review of monoidal categories and their associated graphical languages, we then revisit probability theory from a categorical perspective…

Probability · Mathematics 2013-01-29 Brendan Fong

A structural causal model is made of endogenous (manifest) and exogenous (latent) variables. We show that endogenous observations induce linear constraints on the probabilities of the exogenous variables. This allows to exactly map a causal…

Artificial Intelligence · Computer Science 2020-08-04 Marco Zaffalon , Alessandro Antonucci , Rafael Cabañas

In this paper we present a comprehensive view of prominent causal discovery algorithms, categorized into two main categories (1) assuming acyclic and no latent variables, and (2) allowing both cycles and latent variables, along with…

Artificial Intelligence · Computer Science 2017-09-13 Karamjit Singh , Garima Gupta , Vartika Tewari , Gautam Shroff

We offer a graphical interpretation of unfairness in a dataset as the presence of an unfair causal path in the causal Bayesian network representing the data-generation mechanism. We use this viewpoint to revisit the recent debate…

Machine Learning · Statistics 2019-07-16 Silvia Chiappa , William S. Isaac

A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…

Machine Learning · Computer Science 2022-01-11 David Heckerman

Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…

Machine Learning · Computer Science 2023-01-24 Natraj Raman , Daniele Magazzeni , Sameena Shah

Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…

Methodology · Statistics 2017-06-29 Christina Heinze-Deml , Marloes H. Maathuis , Nicolai Meinshausen

Statistical science (as opposed to mathematical statistics) involves far more than probability theory, for it requires realistic causal models of data generators - even for purely descriptive goals. Statistical decision theory requires more…

Other Statistics · Statistics 2022-06-02 Sander Greenland

In this paper we study the problem of making predictions using multiple structural casual models defined by different agents, under the constraint that the prediction satisfies the criterion of counterfactual fairness. Relying on the…

Artificial Intelligence · Computer Science 2021-05-25 Fabio Massimo Zennaro , Magdalena Ivanovska
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