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.
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.
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)
