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Probabilistic Conditional Independence Structures

By Milan Studeny

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  • ISBN13: 978-1-8523-3891-6
  • 299 Pages
  • User Level: Science
  • Publication Date: June 22, 2006
  • Available eBook Formats: PDF
Full Description
Probabilistic Conditional Independence Structures provides the mathematical description of probabilistic conditional independence structures; the author uses non-graphical methods of their description, and takes an algebraic approach. The monograph presents the methods of structural imsets and supermodular functions, and deals with independence implication and equivalence of structural imsets. Motivation, mathematical foundations and areas of application are included, and a rough overview of graphical methods is also given. In particular, the author has been careful to use suitable terminology, and presents the work so that it will be understood by both statisticians, and by researchers in artificial intelligence. The necessary elementary mathematical notions are recalled in an appendix.
Table of Contents

Table of Contents

  1. Introduction.
  2. Basic Concepts.
  3. Graphical Methods.
  4. Structural Imsets: Fundamentals.
  5. Description of Probabilistic Models.
  6. Equivalence and Implication.
  7. The Problem of Representative Choice.
  8. Learning.
  9. Open Problems.
  10. Appendix.
  11. References.
  12. Index.

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