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On expressiveness of the chain graph interpretations
Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, Faculty of Science & Engineering.
2016 (English)In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 68, 91-107 p.Article in journal (Refereed) PublishedText
Abstract [en]

In this article we study the expressiveness of the different chain graph interpretations. Chain graphs is a class of probabilistic graphical models that can contain two types of edges, representing different types of relationships between the variables in question. Chain graphs is also a superclass of directed acyclic graphs, i.e. Bayesian networks, and can thereby represent systems more accurately than this less expressive class of models. Today there do however exist several different ways of interpreting chain graphs and what conditional independences they encode, giving rise to different so-called chain graph interpretations. Previous research has approximated the number of representable independence models for the Lauritzen-Wermuth-Frydenberg and the multivariate regression chain graph interpretations using an MCMC based approach. In this article we use a similar approach to approximate the number of models representable by the latest chain graph interpretation in research, the Andersson-Madigan-Perlman interpretation. Moreover we summarize and compare the different chain graph interpretations with each other. Our results confirm previous results that directed acyclic graphs only can represent a small fraction of the models representable by chain graphs, even for a low number of nodes. The results also show that the Andersson-Madigan-Perlman and multivariate regression interpretations can represent about the same amount of models and twice the amount of models compared to the Lauritzen-Wermuth-Frydenberg interpretation. However, at the same time almost all models representable by the latter interpretation can only be represented by that interpretation while the former two have a large intersection in terms of representable models. (C) 2015 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE INC , 2016. Vol. 68, 91-107 p.
Keyword [en]
Chain graphs; Lauritzen-Wermuth-Frydenberg interpretation; Andersson-Madigan-Perlman interpretation; Multivariate regression interpretation; MCMC sampling; Expressibility of probabilistic graphical models
National Category
Computer and Information Science
URN: urn:nbn:se:liu:diva-124105DOI: 10.1016/j.ijar.2015.07.009ISI: 000366774200008OAI: diva2:897183

Funding Agencies|Swedish Research Council [2010-4808]

Available from: 2016-01-25 Created: 2016-01-19 Last updated: 2016-03-29
In thesis
1. Chain Graphs: Interpretations, Expressiveness and Learning Algorithms
Open this publication in new window or tab >>Chain Graphs: Interpretations, Expressiveness and Learning Algorithms
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Probabilistic graphical models are currently one of the most commonly used architectures for modelling and reasoning with uncertainty. The most widely used subclass of these models is directed acyclic graphs, also known as Bayesian networks, which are used in a wide range of applications both in research and industry. Directed acyclic graphs do, however, have a major limitation, which is that only asymmetric relationships, namely cause and effect relationships, can be modelled between their variables. A class of probabilistic graphical models that tries to address this shortcoming is chain graphs, which include two types of edges in the models representing both symmetric and asymmetric relationships between the variables. This allows for a wider range of independence models to be modelled and depending on how the second edge is interpreted, we also have different so-called chain graph interpretations.

Although chain graphs were first introduced in the late eighties, most research on probabilistic graphical models naturally started in the least complex subclasses, such as directed acyclic graphs and undirected graphs. The field of chain graphs has therefore been relatively dormant. However, due to the maturity of the research field of probabilistic graphical models and the rise of more data-driven approaches to system modelling, chain graphs have recently received renewed interest in research. In this thesis we provide an introduction to chain graphs where we incorporate the progress made in the field. More specifically, we study the three chain graph interpretations that exist in research in terms of their separation criteria, their possible parametrizations and the intuition behind their edges. In addition to this we also compare the expressivity of the interpretations in terms of representable independence models as well as propose new structure learning algorithms to learn chain graph models from data.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2016. 44 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1748
Chain Graphs, Probabilitstic Grapical Models
National Category
Computer Systems
urn:nbn:se:liu:diva-125921 (URN)10.3384/diss.diva-125921 (DOI)978-91-7685-818-9 (Print) (ISBN)
Public defence
2016-04-29, Visionen, B-House, Entrance 27, Campus Valla, Linköping, 13:15 (English)
Swedish Research Council, 2010-4808
Available from: 2016-03-29 Created: 2016-03-08 Last updated: 2016-03-29Bibliographically approved

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