Probabilistic Conditional Independence Structures

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.

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

Zusammenfassung
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.

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