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Probabilistic Conditional Independence Structures

  • Book
  • © 2005

Overview

Authors:
  1. Milan Studený

    1. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague 8, Libeň, Czech Republic

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Editors:
  1. Michael Jordan

    1. Division of Computer Science and Department of Statistics, University of California, Berkeley, Berkeley, USA

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  2. Jon Kleinberg

    1. Department of Computer Science, Cornell University, Ithaca, USA

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  3. Bernhard Schölkopf

    1. Max Planck Institute for Biological Cybernetics, Tübingen, Germany

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  4. Frank P. Kelly

    1. Statistical Laboratory, Centre for Mathematical Sciences, Cambridge, UK

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  5. Ian Witten

    1. Department of Computer Science, University of Waikato, Hamilton, New Zealand

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  • Written by the world’s leading expert on conditional independence structures
  • It is the first book to use non-graphical methods in this subject
  • Self-contained: a comprehensive survey of the necessary mathematical and statistical background is provided in an appendix
  • Designed to be accessible to both statisticians, and researchers in artificial intelligence
  • Includes supplementary material: sn.pub/extras

Part of the book series: Information Science and Statistics (ISS)

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About this book

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.

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Keywords

Table of contents (9 chapters)

  1. Front Matter

    Pages I-XIV
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  2. Introduction

    Pages 1-8

  3. Basic Concepts

    Pages 9-41

  4. Graphical Methods

    Pages 43-64

  5. Structural Imsets: Fundamentals

    Pages 65-86

  6. Description of Probabilistic Models

    Pages 87-109

  7. Equivalence and Implication

    Pages 111-129

  8. The Problem of Representative Choice

    Pages 131-154

  9. Learning

    Pages 155-188

  10. Open Problems

    Pages 189-214

  11. Back Matter

    Pages 215-285
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Reviews

From the reviews:

"This monograph aims to present methods of structural imsets and supermodel functions and considers the independence implication and equivalence of structural imsets. Dr. Studeny also looks at motivation, mathematical foundations and areas of application. … The book has been prepared so that it will be understood by statisticians but also by researchers, particularly … by those involved in Artificial intelligence. The Appendix, listed with the contents contains … all the necessary elementary mathematical notions that may be required or recalled." (Kybernetes, Vol. 34 (7-8), 2005)

"This monograph is a self-contained, unified mathematical treatment of basic results in the mathematical description of probabilistic conditional independence structures. … This monograph provides graduate students with a sound basis for further study and for research and is a valuable reference source for both statisticians and researchers in artificial intelligence." (J. Martyna, Zentralblatt MATH, Vol. 1070, 2005)

Authors, Editors and Affiliations

  • Division of Computer Science and Department of Statistics, University of California, Berkeley, Berkeley, USA

    Michael Jordan

  • Department of Computer Science, Cornell University, Ithaca, USA

    Jon Kleinberg

  • Max Planck Institute for Biological Cybernetics, Tübingen, Germany

    Bernhard Schölkopf

  • Statistical Laboratory, Centre for Mathematical Sciences, Cambridge, UK

    Frank P. Kelly

  • Department of Computer Science, University of Waikato, Hamilton, New Zealand

    Ian Witten

  • Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague 8, Libeň, Czech Republic

    Milan Studený

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