Probabilistic conditional independence structures
By: Milan Studený.
Series: Information science and statistics
Publisher: Springer
Published: 2005
Place of publication: London
Language: eng
Number of pages: 285
Subjects: Statistics -- Graphic methods; Distribution (Probability theory); Artificial intelligence -- Mathematical models; Decision making -- Mathematical models
Description: 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.
Notes: Includes bibliographical references (p. [263]-271) and index.