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2013 | OriginalPaper | Chapter

22. Elements of Probability and Graph Theory

Authors : Rudolf Kruse, Christian Borgelt, Frank Klawonn, Christian Moewes, Matthias Steinbrecher, Pascal Held

Published in: Computational Intelligence

Publisher: Springer London

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Abstract

This chapter introduces required theoretical concepts for the definition of Bayes and Markov networks. After important elements of probability theory—especially (conditional) independences—are discussed, we present relevant graph-theoretic notions with emphasis on so-called separation criteria. These criteria will later allow us to capture probabilistic independences with an undirected or directed graph.

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previous chapter Introduction to Bayes Networks
next chapter Decompositions
Literature
E. Castillo, J.M. Gutierrez, and A.S. Hadi. Expert Systems and Probabilistic Network Models. Springer-Verlag, New York, NY, USA, 1997 CrossRef
F.V. Jensen. Junction Trees and Decomposable Hypergraphs. Research Report, JUDEX Data Systems, Aalborg, Denmark, 1988
A.N. Kolmogorov. Grundbegriffe der WahrScheinLichKeitsRechnung. Springer-Verlag, Heidelberg, 1933. English edition: Foundations of the Theory of Probability. Chelsea, New York, NY, USA, 1956
J.B. Kruskal. On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem. Proceedings of the American Mathematical Society 7(1):48–50. American Mathematical Society, Providence, RI, USA, 1956 MathSciNetMATHCrossRef
S.L. Lauritzen and D.J. Spiegelhalter. Local Computations with Probabilities on Graphical Structures and Their Application to Expert Systems. Journal of the Royal Statistical Society, Series B 2(50):157–224. Blackwell, Oxford, United Kingdom, 1988 MathSciNet
R.C. Prim. Shortest Connection Networks and Some Generalizations. The Bell System Technical Journal 36:1389–1401. Bell Laboratories, Murray Hill, NJ, USA, 1957
Metadata
Title
Elements of Probability and Graph Theory
Authors
Rudolf Kruse
Christian Borgelt
Frank Klawonn
Christian Moewes
Matthias Steinbrecher
Pascal Held
Copyright Year
2013
Publisher
Springer London
Book
Computational Intelligence

Print ISBN: 978-1-4471-5012-1

Electronic ISBN: 978-1-4471-5013-8

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-1-4471-5013-8_22

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