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Learning Multivariate Regression Chain Graphs under Faithfulness
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. (ADIT)
2012 (English)In: Proceedings of the 6th European Workshop on Probabilistic Graphical Models, Granada (Spain), 19-21 September, 2012 / [ed] Andrés Cano, Manuel Gémez.-Olmedo and Thomas D. Nielsen, 2012, 299-306 p.Conference paper, Published paper (Refereed)
Abstract [en]

This paper deals with multivariate regression chain graphs, which were introduced by Cox and Wermuth (1993, 1996) to represent linear causal models with correlated errors. Specifically, we present a constraint based algorithm for learning a chain graph a given probability distribution is faithful to. We also show that for each Markov equivalence class of multivariate regression chain graphs there exists a set of chain graphs with a unique minimal set of lines. Finally, we show that this set of lines can be identified from any member of the class by repeatedly splitting its connectivity components according to certain conditions.

Place, publisher, year, edition, pages
2012. 299-306 p.
Keyword [en]
Chain Graph, Multivariate Regression Chain Graph, Learning, Bidirected Graph
National Category
Computer Systems
Identifiers
URN: urn:nbn:se:liu:diva-80306ISBN: 978-84-15536-57-4 (print)OAI: oai:DiVA.org:liu-80306DiVA: diva2:546468
Conference
Sixth European Workshop on Probabilistic Graphical Models (PGM 2012), 19-21 September 2012, Granada, Spain
Available from: 2012-08-23 Created: 2012-08-23 Last updated: 2016-07-01Bibliographically approved
In thesis
1. A Study of Chain Graph Interpretations
Open this publication in new window or tab >>A Study of Chain Graph Interpretations
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Probabilistic graphical models are today one of the most well used architectures for modelling and reasoning about knowledge with uncertainty. The most widely used subclass of these models is Bayesian networks that has found a wide range of applications both in industry and research. Bayesian networks do however have a major limitation which is that only asymmetric relationships, namely cause and eect relationships, can be modelled between its variables. A class of probabilistic graphical models that has tried to solve this shortcoming is chain graphs. It is achieved by including two types of edges in the models, representing both symmetric and asymmetric relationships between the connected variables. This allows for a wider range of independence models to be modelled. Depending on how the second edge is interpreted this has also given rise to dierent chain graph interpretations.

Although chain graphs were first presented in the late eighties the field has been relatively dormant and most research has been focused on Bayesian networks. This was until recently when chain graphs got renewed interest. The research on chain graphs has thereafter extended many of the ideas from Bayesian networks and in this thesis we study what this new surge of research has been focused on and what results have been achieved. Moreover we do also discuss what areas that we think are most important to focus on in further research.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2014. 161 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1647
National Category
Computer Systems
Identifiers
urn:nbn:se:liu:diva-105024 (URN)10.3384/lic.diva-105024 (DOI)978-91-7519-377-9 (ISBN)
Presentation
2014-04-29, Alan Turing, Hus E, Campus Valla, Linköping University, Linköping, 13:15 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 2010-4808
Available from: 2014-04-08 Created: 2014-03-06 Last updated: 2014-04-08Bibliographically approved
2. 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.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1748
Keyword
Chain Graphs, Probabilitstic Grapical Models
National Category
Computer Systems
Identifiers
urn:nbn:se:liu:diva-125921 (URN)10.3384/diss.diva-125921 (DOI)978-91-7685-818-9 (ISBN)
Public defence
2016-04-29, Visionen, B-House, Entrance 27, Campus Valla, Linköping, 13:15 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 2010-4808
Available from: 2016-03-29 Created: 2016-03-08 Last updated: 2016-03-29Bibliographically approved

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Sonntag, DagPeña, Jose M.

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