Ebook: On Probabilistic Conditional Independence Structures
- Tags: Artificial Intelligence (incl. Robotics), Statistics for Engineering Physics Computer Science Chemistry & Geosciences
- Series: Information Science and Statistics
- Year: 2005
- Publisher: Springer-Verlag London
- Edition: 1
- Language: English
- pdf
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.
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 Studen? is a senior research worker at the Academy of Sciences of the Czech Republic.
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 Studen? is a senior research worker at the Academy of Sciences of the Czech Republic.
Content:
Front Matter....Pages I-XIV
Introduction....Pages 1-8
Basic Concepts....Pages 9-41
Graphical Methods....Pages 43-64
Structural Imsets: Fundamentals....Pages 65-86
Description of Probabilistic Models....Pages 87-109
Equivalence and Implication....Pages 111-129
The Problem of Representative Choice....Pages 131-154
Learning....Pages 155-188
Open Problems....Pages 189-214
Back Matter....Pages 215-285
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 Studen? is a senior research worker at the Academy of Sciences of the Czech Republic.
Content:
Front Matter....Pages I-XIV
Introduction....Pages 1-8
Basic Concepts....Pages 9-41
Graphical Methods....Pages 43-64
Structural Imsets: Fundamentals....Pages 65-86
Description of Probabilistic Models....Pages 87-109
Equivalence and Implication....Pages 111-129
The Problem of Representative Choice....Pages 131-154
Learning....Pages 155-188
Open Problems....Pages 189-214
Back Matter....Pages 215-285
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