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Information Algebras: Generic Structures For Inference: Discrete Mathematics and Theoretical Computer Science

Autor Juerg Kohlas
en Limba Engleză Paperback – 5 dec 2002
Information usually comes in pieces, from different sources. It refers to different, but related questions. Therefore information needs to be aggregated and focused onto the relevant questions. Considering combination and focusing of information as the relevant operations leads to a generic algebraic structure for information. This book introduces and studies information from this algebraic point of view. Algebras of information provide the necessary abstract framework for generic inference procedures. They allow the application of these procedures to a large variety of different formalisms for representing information. At the same time they permit a generic study of conditional independence, a property considered as fundamental for knowledge presentation. Information algebras provide a natural framework to define and study uncertain information. Uncertain information is represented by random variables that naturally form information algebras. This theory also relates to probabilistic assumption-based reasoning in information systems and is the basis for the belief functions in the Dempster-Shafer theory of evidence.
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Specificații

ISBN-13: 9781852336899
ISBN-10: 1852336897
Pagini: 280
Ilustrații: X, 265 p.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 0.4 kg
Ediția:Softcover reprint of the original 1st ed. 2003
Editura: SPRINGER LONDON
Colecția Springer
Seria Discrete Mathematics and Theoretical Computer Science

Locul publicării:London, United Kingdom

Public țintă

Research

Cuprins

1 Introduction.- 2 Valuation Algebras.- 2.1 The Framework.- 2.2 Axioms.- 2.3 Examples of Valuation Algebras.- 2.4 Partial Marginalization.- 3 Algebraic Theory.- 3.1 Congruences.- 3.2 Domain-Free Valuation Algebras.- 3.3 Subalgebras, Homomorphisms.- 3.4 Null Valuations.- 3.5 Regular Valuation Algebras.- 3.6 Separative Valuation Algebras.- 3.7 Scaled Valuation Algebras.- 4 Local Computation.- 4.1 Fusion Algorithm.- 4.2 Collect Algorithm.- 4.3 Computing Multiple Marginals.- 4.4 Architectures with Division.- 4.5 Computations in Valuation Algebras with Partial Marginalization.- 4.6 Scaling and Updating.- 5 Conditional Independence.- 5.1 Factorization and Graphical Models.- 5.2 Conditionals in Regular Algebras.- 5.3 Conditionals in Separative Algebras.- 6 Information Algebras.- 6.1 Idempotency.- 6.2 Partial Order of Information.- 6.3 File Systems.- 6.4 Information Systems.- 6.5 Examples.- 6.6 Compact Systems.- 6.7 Mappings.- 7 Uncertain Information.- 7.1 Algebra of Random Variables.- 7.2 Probabilistic Argumentation Systems.- 7.3 Allocations of Probability.- 7.4 Independent Sources.- References.

Caracteristici

For the first time the common, abstract and unifying algebraic structure underlying different inference algorithms as used in Bayesian networks, possibility theory, Dempster-Shafer theory, logic, linear systems (sparse matrices) is presented in book form Includes supplementary material: sn.pub/extras