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
Conditional independence is a topic that lies between statistics and artificial intelligence. Probabilistic Conditional Independence Structures provides the mathematical deillegalscription of probabilistic conditional independence structures; the author uses non-graphical methods of their deillegalscription, 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.
Basic Concepts.- Graphical Methods.- Structural Imsets: Fundamentals.- Deillegalscription of Probabilistic Models.- Equivalence and Implication.- The Problem of Representative Choice.- Learning.- Open Problems.
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 deillegalscription 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)
Probabilistic Conditional Independence Structures provides the mathematical deillegalscription of probabilistic conditional independence structures; the author uses non-graphical methods of their deillegalscription, 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.
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 deillegalscription 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)
Conditional independence is a topic that lies between statistics and artificial intelligence. Probabilistic Conditional Independence Structures provides the mathematical deillegalscription of probabilistic conditional independence structures; the author uses non-graphical methods of their deillegalscription, 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.
Inhaltsverzeichnis
Introduction.- Basic Concepts.- Graphical Methods.- Structural Imsets: Fundamentals.- Deillegalscription of Probabilistic Models.- Equivalence and Implication.- The Problem of Representative Choice.- Learning.- Open Problems.- Appendix.- References.- Index.
Klappentext
Probabilistic Conditional Independence Structures provides the mathematical deillegalscription of probabilistic conditional independence structures; the author uses non-graphical methods of their deillegalscription, 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 deillegalscription of probabilistic conditional independence structures; the author uses non-graphical methods of their deillegalscription, 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.
