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Decompositions

  • Rudolf Kruse
  • Christian Borgelt
  • Frank Klawonn
  • Christian Moewes
  • Matthias Steinbrecher
  • Pascal Held
Chapter
Part of the Texts in Computer Science book series (TCS)

Abstract

The objective of this chapter is to connect the concepts of conditional independence with the separation in graphs. Both can be represented by a ternary relation Open image in new window on either the set of attributes or nodes and it seems to be promising to investigate how to represent the probabilistic properties of a distribution by the means of a graph. The idea then is to use only graph-theoretic criteria (separations) to draw inferences about (conditional) independences because it is them what enables us to decompose a high-dimensional distribution and propagate evidence.

References

  1. C. Borgelt, M. Steinbrecher, and R. Kruse. Graphical Models—Representations for Learning, Reasoning and Data Mining, 2nd ed. J. Wiley & Sons, Chichester, United Kingdom, 2009 zbMATHGoogle Scholar
  2. A.P. Dawid. Conditional Independence in Statistical Theory. Journal of the Royal Statistical Society, Series B (Methodological) 41(1):1–31. Blackwell, Oxford, United Kingdom, 1979 MathSciNetzbMATHGoogle Scholar
  3. J. Gebhardt and R. Kruse. Knowledge-Based Operations for Graphical Models in Planning. Proc. Europ. Conf. on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2005, Barcelona, Spain), LNAI 3571:3–14. Springer-Verlag, Berlin, Germany, 2005 CrossRefGoogle Scholar
  4. J. Gebhardt, H. Detmer, and A.L. Madsen. Predicting Parts Demand in the Automotive Industry—An Application of Probabilistic Graphical Models. Proc. Bayesian Modelling Applications Workshop at Int. Joint Conf. on Uncertainty in Artificial Intelligence (UAI 2003, Acapulco, Mexico), 2003 Google Scholar
  5. J. Gebhardt, C. Borgelt, R. Kruse, and H. Detmer. Knowledge Revision in Markov Networks. Mathware and Soft Computing 11(2–3):93–107. University of Granada, Granada, Spain, 2004 MathSciNetzbMATHGoogle Scholar
  6. J. Gebhardt, A. Klose, H. Detmer, F. Rügheimer, and R. Kruse. Graphical Models for Industrial Planning on Complex Domains. In: D. Della Riccia, D. Dubois, R. Kruse, and H.-J. Lenz (eds.) Decision Theory and Multi-Agent Planning, CISM Courses and Lectures 482:131–143. Springer-Verlag, Berlin, Germany, 2006 CrossRefGoogle Scholar
  7. J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo, CA, USA, 1988 Google Scholar
  8. J. Pearl and A. Paz. Graphoids: A Graph Based Logic for Reasoning About Relevance Relations. In: B.D. Boulay, D. Hogg, and L. Steels (eds.) Advances in Artificial Intelligence 2, 357–363. North Holland, Amsterdam, Netherlands, 1987 Google Scholar
  9. M. Studeny. Multiinformation and the Problem of Characterization of Conditional Independence Relations. Problems of Control and Information Theory 1:3–16, 1989 MathSciNetGoogle Scholar
  10. M. Studeny. Conditional Independence Relations Have No Finite Complete Characterization. Kybernetika 25:72–79. Institute of Information Theory and Automation, Prague, Czech Republic, 1990 MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Rudolf Kruse
    • 1
  • Christian Borgelt
    • 2
  • Frank Klawonn
    • 3
  • Christian Moewes
    • 1
  • Matthias Steinbrecher
    • 4
  • Pascal Held
    • 1
  1. 1.Faculty of Computer ScienceOtto-von-Guericke University MagdeburgMagdeburgGermany
  2. 2.Intelligent Data Analysis & Graphical Models Research UnitEuropean Centre for Soft ComputingMieresSpain
  3. 3.FB InformatikOstfalia University of Applied SciencesWolfenbüttelGermany
  4. 4.SAP Innovation CenterPotsdamGermany

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