Probabilistic Conditional Independence Structures

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)

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