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Concentrated or non-concentrated discrete distributions are almost independent
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.ORCID iD: 0000-0001-9896-4438
2007 (English)Manuscript (preprint) (Other academic)
Abstract [en]

The task of approximating a simultaneous distribution with a product of distributions in a single variable is important in the theory and applications of classification and learning, probabilistic reasoning, and random algmithms. The evaluation of the goodness of this approximation by statistical independence amounts to bounding uniformly upwards the difference between a joint distribution and the product of the distributions (marginals). In this paper we develop a bound that uses information about the most probable state to find a sharp estimate, which is often as sharp as possible. We also examine the extreme cases of concentration and non-conccntmtion, respectively, of the approximated distribution.

Place, publisher, year, edition, pages
2007.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-13105OAI: oai:DiVA.org:liu-13105DiVA: diva2:17843
Available from: 2008-03-31 Created: 2008-03-31 Last updated: 2014-09-29
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, TimoOhlson, Martin

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