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Chain graph interpretations and their relations revisited
Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, The Institute of Technology.
Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, The Institute of Technology.
2015 (English)In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 58, 39-56 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we study how different theoretical concepts of Bayesian networks have been extended to chain graphs. Today there exist mainly three different interpretations of chain graphs in the literature. These are the Lauritzen-Wermuth-Frydenberg, the Andersson-Madigan-Perlman and the multivariate regression interpretations. The different chain graph interpretations have been studied independently and over time different theoretical concepts have been extended from Bayesian networks to also work for the different chain graph interpretations. This has however led to confusion regarding what concepts exist for what interpretation. In this article we do therefore study some of these concepts and how they have been extended to chain graphs as well as what results have been achieved so far. More importantly we do also identify when the concepts have not been extended and contribute within these areas. Specifically we study the following theoretical concepts: Unique representations of independence models, the split and merging operators, the conditions for when an independence model representable by one chain graph interpretation can be represented by another chain graph interpretation and finally the extension of Meeks conjecture to chain graphs. With our new results we give a coherent overview of how each of these concepts is extended for each of the different chain graph interpretations.

Place, publisher, year, edition, pages
Elsevier , 2015. Vol. 58, 39-56 p.
Keyword [en]
Chain graphs; Lauritzen-Wermuth-Frydenberg interpretation; Andersson-Madigan-Perlman interpretation; Multivariate regression interpretation
National Category
Computer and Information Science
URN: urn:nbn:se:liu:diva-116826DOI: 10.1016/j.ijar.2014.12.001ISI: 000350516100004OAI: diva2:800745

Funding Agencies|Center for Industrial Information Technology (CENIIT); Swedish Research Council [2010-4808]; FEDER funds; Spanish Government (MICINN) [TIN2010-20900-004-03]

Available from: 2015-04-07 Created: 2015-04-07 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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