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Entropy
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Causal Graphical Models and Their Applications
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Causal Graphical Models and Their Applications

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (31 March 2025) | Viewed by 4725

Special Issue Editors

Dr. Luis Enrique Sucar

E-Mail Website
Guest Editor
Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Santa María Tonantzintla, Puebla 72840, Mexico
Interests: probabilistic reasoning in artificial intelligence; computer vision and image processing; service robots; causal graphical models; causal discovery
Prof. Dr. David Danks

E-Mail Website
Guest Editor
The Halıcıoğlu Data Science Institute, University of California, San Diego, CA 92093, USA
Interests: causal learning; time series; cognitive science; AI ethics

Special Issue Information

Dear Colleagues,

The concept of causality deals with the regularities found in a given environment that have stronger than probabilistic (or associative) relations, in the sense that a causal relation allows for evaluating a change in the consequence given a change in the cause. Recently, there has been an increasing interest in causal models, in particular causal graphical models, since several cognitive processes, such as causal reasoning, can be best represented as graphical models. Causal models, in contrast with traditional associative models, provide a more powerful representation that can be used for reasoning about interventions and counterfactuals. They can also help us to build more transparent and robust intelligent systems and provide explanations. A challenging problem is to create these models using observational data, known as causal discovery, an active research area. These models are being applied in different fields, such as biology, medicine, and economics, among others.

The objective of this Special Issue is to present recent advances in causal reasoning and causal discovery based on causal graphical models, including novel applications in different domains.

Dr. Luis Enrique Sucar
Prof. Dr. David Danks
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • causal graphical models
  • causal reasoning
  • causal discovery
  • applications of causal models

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Published Papers (4 papers)

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19 pages, 402 KiB  
Article
A Novel Hyper-Heuristic Algorithm with Soft and Hard Constraints for Causal Discovery Using a Linear Structural Equation Model
by Yinglong Dang, Xiaoguang Gao and Zidong Wang
Entropy 2025, 27(1), 38; https://doi.org/10.3390/e27010038 - 6 Jan 2025
Viewed by 887
Abstract
Artificial intelligence plays an indispensable role in improving productivity and promoting social development, and causal discovery is one of the extremely important research directions in this field. Acyclic directed graphs (DAGs) are the most commonly used tool in causal modeling because of their [...] Read more.
Artificial intelligence plays an indispensable role in improving productivity and promoting social development, and causal discovery is one of the extremely important research directions in this field. Acyclic directed graphs (DAGs) are the most commonly used tool in causal modeling because of their excellent interpretability and structural properties. However, in the face of insufficient data, the accuracy and efficiency of DAGs learning are greatly reduced, resulting in a false perception of causality. As intuitive expert knowledge, structural constraints control DAG learning by limiting the causal relationship between variables, which is expected to solve the above-mentioned problem. However, it is often impossible to build a DAG by relying on expert knowledge alone. To solve this problem, we propose the use of expert knowledge as a hard constraint and the structural prior gained via data learning as a soft constraint. In this paper, we propose a fitness-rate-rank-based multiarmed bandit (FRRMAB) hyper-heuristic that integrates soft and hard constraints into the DAG learning process. For a linear structural equation model (SEM), soft constraints are obtained via partial correlation analysis. The experimental results on different networks show that the proposed method has higher scalability and accuracy. Full article
(This article belongs to the Special Issue Causal Graphical Models and Their Applications)
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27 pages, 428 KiB  
Article
Identifying Causal Effects Under Functional Dependencies
by Yizuo Chen and Adnan Darwiche
Entropy 2024, 26(12), 1061; https://doi.org/10.3390/e26121061 - 6 Dec 2024
Cited by 1 | Viewed by 756
Abstract
We study the identification of causal effects, motivated by two improvements to identifiability that can be attained if one knows that some variables in a causal graph are functionally determined by their parents (without needing to know the specific functions). First, an unidentifiable [...] Read more.
We study the identification of causal effects, motivated by two improvements to identifiability that can be attained if one knows that some variables in a causal graph are functionally determined by their parents (without needing to know the specific functions). First, an unidentifiable causal effect may become identifiable when certain variables are functional. Secondly, certain functional variables can be excluded from being observed without affecting the identifiability of a causal effect, which may significantly reduce the number of needed variables in observational data. Our results are largely based on an elimination procedure that removes functional variables from a causal graph while preserving key properties in the resulting causal graph, including the identifiability of causal effects. Our treatment of functional dependencies in this context mandates a formal, systematic, and general treatment of positivity assumptions, which are prevalent in the literature on causal effect identifiability and which interact with functional dependencies, leading to another contribution of the presented work. Full article
(This article belongs to the Special Issue Causal Graphical Models and Their Applications)
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18 pages, 592 KiB  
Article
Causal Learning: Monitoring Business Processes Based on Causal Structures
by Fernando Montoya, Hernán Astudillo, Daniela Díaz and Esteban Berríos
Entropy 2024, 26(10), 867; https://doi.org/10.3390/e26100867 - 15 Oct 2024
Viewed by 1324
Abstract
Conventional methods for process monitoring often fail to capture the causal relationships that drive outcomes, making hard to distinguish causal anomalies from mere correlations in activity flows. Hence, there is a need for approaches that allow causal interpretation of atypical scenarios (anomalies), allowing [...] Read more.
Conventional methods for process monitoring often fail to capture the causal relationships that drive outcomes, making hard to distinguish causal anomalies from mere correlations in activity flows. Hence, there is a need for approaches that allow causal interpretation of atypical scenarios (anomalies), allowing to identify the influence of operational variables on these anomalies. This article introduces (CaProM), an innovative technique based on causality techniques, applied during the planning phase in business process environments. The technique combines two causal perspectives: anomaly attribution and distribution change attribution. It has three stages: (1) process events are collected and recorded, identifying flow instances; (2) causal learning of process activities, building a directed acyclic graphs (DAGs) represent dependencies among variables; and (3) use of DAGs to monitor the process, detecting anomalies and critical nodes. The technique was validated with a industry dataset from the banking sector, comprising 562 activity flow plans. The study monitored causal structures during the planning and execution stages, and allowed to identify the main factor behind a major deviation from planned values. This work contributes to business process monitoring by introducing a causal approach that enhances both the interpretability and explainability of anomalies. The technique allows to understand which specific variables have caused an atypical scenario, providing a clear view of the causal relationships within processes and ensuring greater accuracy in decision-making. This causal analysis employs cross-sectional data, avoiding the need to average multiple time instances and reducing potential biases, and unlike time series methods, it preserves the relationships among variables. Full article
(This article belongs to the Special Issue Causal Graphical Models and Their Applications)
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Other

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43 pages, 735 KiB  
Systematic Review
Causal Artificial Intelligence in Legal Language Processing: A Systematic Review
by Philippe Prince Tritto and Hiram Ponce
Entropy 2025, 27(4), 351; https://doi.org/10.3390/e27040351 - 28 Mar 2025
Viewed by 767
Abstract
Recent advances in legal language processing have highlighted limitations in correlation-based artificial intelligence approaches, prompting exploration of Causal Artificial Intelligence (AI) techniques for improved legal reasoning. This systematic review examines the challenges, limitations, and potential impact of Causal AI in legal language processing [...] Read more.
Recent advances in legal language processing have highlighted limitations in correlation-based artificial intelligence approaches, prompting exploration of Causal Artificial Intelligence (AI) techniques for improved legal reasoning. This systematic review examines the challenges, limitations, and potential impact of Causal AI in legal language processing compared to traditional correlation-based methods. Following the Joanna Briggs Institute methodology, we analyzed 47 papers from 2017 to 2024 across academic databases, private sector publications, and policy documents, evaluating their contributions through a rigorous scoring framework assessing Causal AI implementation, legal relevance, interpretation capabilities, and methodological quality. Our findings reveal that while Causal AI frameworks demonstrate superior capability in capturing legal reasoning compared to correlation-based methods, significant challenges remain in handling legal uncertainty, computational scalability, and potential algorithmic bias. The scarcity of comprehensive real-world implementations and overemphasis on transformer architectures without causal reasoning capabilities represent critical gaps in current research. Future development requires balanced integration of AI innovation with law’s narrative functions, particularly focusing on scalable architectures for maintaining causal coherence while preserving interpretability in legal analysis. Full article
(This article belongs to the Special Issue Causal Graphical Models and Their Applications)
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