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Parallell interacting MCMC for learning of topologies of graphical models
Department of Mathematics, Åbo Akademi University, Åbo, Finland.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden.
2008 (English)In: Data mining and knowledge discovery, ISSN 1384-5810, E-ISSN 1573-756X, Vol. 17, no 3, 431-456 p.Article in journal (Refereed) Published
Abstract [en]

Automated statistical learning of graphical models from data has attained a considerable degree of interest in the machine learning and related literature. Many authors have discussed and/or demonstrated the need for consistent stochastic search methods that would not be as prone to yield locally optimal model structures as simple greedy methods. However, at the same time most of the stochastic search methods are based on a standard Metropolis–Hastings theory that necessitates the use of relatively simple random proposals and prevents the utilization of intelligent and efficient search operators. Here we derive an algorithm for learning topologies of graphical models from samples of a finite set of discrete variables by utilizing and further enhancing a recently introduced theory for non-reversible parallel interacting Markov chain Monte Carlo-style computation. In particular, we illustrate how the non-reversible approach allows for novel type of creativity in the design of search operators. Also, the parallel aspect of our method illustrates well the advantages of the adaptive nature of search operators to avoid trapping states in the vicinity of locally optimal network topologies.

Place, publisher, year, edition, pages
2008. Vol. 17, no 3, 431-456 p.
Keyword [en]
MCMC, Equivalence search, Learning graphical models
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-13106DOI: 10.1007/s10618-008-0099-9OAI: oai:DiVA.org:liu-13106DiVA: diva2:17844
Available from: 2008-03-31 Created: 2008-03-31 Last updated: 2017-12-13
In thesis
1. On approximations and computations in probabilistic classification and in learning of graphical models
Open this publication in new window or tab >>On approximations and computations in probabilistic classification and in learning of graphical models
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Model based probabilistic classification is heavily used in data mining and machine learning. For computational learning these models may need approximation steps however. One popular approximation in classification is to model the class conditional densities by factorization, which in the independence case is usually called the ’Naïve Bayes’ classifier. In general probabilistic independence cannot model all distributions exactly, and not much has been published on how much a discrete distribution can differ from the independence assumption. In this dissertation the approximation quality of factorizations is analyzed in two articles.

A specific class of factorizations is the factorizations represented by graphical models. Several challenges arise from the use of statistical methods for learning graphical models from data. Examples of problems include the increase in the number of graphical model structures as a function of the number of nodes, and the equivalence of statistical models determined by different graphical models. In one article an algorithm for learning graphical models is presented. In the final article an algorithm for clustering parts of DNA strings is developed, and a graphical representation for the remaining DNA part is learned.

Place, publisher, year, edition, pages
Matematiska institutionen, 2007. 22 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1141
Keyword
Mathematical statistics, factorizations, probabilistic classification, nodes, DNA strings
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-11429 (URN)978-91-85895-58-8 (ISBN)
Public defence
2007-12-14, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Available from: 2008-03-31 Created: 2008-03-31 Last updated: 2012-11-21

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Ekdahl, MagnusKoski, Timo

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