On Probabilistic Conditional Independence Structures

  • Milan Studený
  • Michael Jordan
  • Jon Kleinberg
  • Bernhard Schölkopf
  • Frank P. Kelly
  • Ian Witten

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

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Pages 1-8
  3. Pages 9-41
  4. Pages 43-64
  5. Pages 155-188
  6. Pages 189-214
  7. Back Matter
    Pages 215-285

About this book

Introduction

Conditional independence is a topic that lies between statistics and artificial intelligence. 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.

Probabilistic Conditional Independence Structures will be a valuable new addition to the literature, and will interest applied mathematicians, statisticians, informaticians, computer scientists and probabilists with an interest in artificial intelligence. The book may also interest pure mathematicians as open problems are included.

Milan Studený is a senior research worker at the Academy of Sciences of the Czech Republic.

Keywords

Mathematica algebra artificial intelligence computer function intelligence learning statistics

Authors and affiliations

  • Milan Studený
    • 1
  1. 1.Institute of Information Theory and AutomationAcademy of Sciences of the Czech RepublicPrague 8, LibeňCzech Republic

Editors and affiliations

  • Michael Jordan
    • 1
  • Jon Kleinberg
    • 2
  • Bernhard Schölkopf
    • 3
  • Frank P. Kelly
    • 4
  • Ian Witten
    • 5
  1. 1.Division of Computer Science and Department of StatisticsUniversity of California, BerkeleyBerkeleyUSA
  2. 2.Department of Computer ScienceCornell UniversityIthacaUSA
  3. 3.Max Planck Institute for Biological CyberneticsTübingenGermany
  4. 4.Statistical LaboratoryCentre for Mathematical SciencesCambridgeUK
  5. 5.Department of Computer ScienceUniversity of WaikatoHamiltonNew Zealand

Bibliographic information

  • DOI https://doi.org/10.1007/b138557
  • Copyright Information Springer-Verlag London Limited 2005
  • Publisher Name Springer, London
  • eBook Packages Computer Science
  • Print ISBN 978-1-85233-891-6
  • Online ISBN 978-1-84628-083-2
  • Series Print ISSN 1613-9011
  • About this book