Probabilistic Conditional Independence Structures / Edition 1

Probabilistic Conditional Independence Structures / Edition 1

by Milan Studeny
     
 

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

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Overview

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.

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Product Details

ISBN-13:
9781849969482
Publisher:
Springer London
Publication date:
12/13/2010
Series:
Information Science and Statistics Series
Edition description:
Softcover reprint of hardcover 1st ed. 2005
Pages:
285
Product dimensions:
0.63(w) x 6.14(h) x 9.21(d)

Table of Contents

Introduction.- Basic Concepts.- Graphical Methods.- Structural Imsets: Fundamentals.- Description of Probabilistic Models.- Equivalence and Implication.- The Problem of Representative Choice.- Learning.- Open Problems.- Appendix.- References.- Index.

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