Information Algebras: Generic Structures For Inference - Softcover

Inhaltsangabe

1 Introduction.- 2 Valuation Algebras.- 2.1 The Framework.- 2.2 Axioms.- 2.3 Examples of Valuation Algebras.- 2.3.1 Indicator Functions.- 2.3.2 Relations.- 2.3.3 Probability Potentials.- 2.3.4 Possibility Potentials.- 2.3.5 Spohn Potentials.- 2.3.6 Set Potentials.- 2.3.7 Gaussian Potentials.- 2.4 Partial Marginalization.- 3 Algebraic Theory.- 3.1 Congruences.- 3.2 Domain-Free Valuation Algebras.- 3.3 Subalgebras, Homomorphisms.- 3.3.1 Subalgebras.- 3.3.2 Homomorphisms and Isomorphisms.- 3.3.3 Weak Subalgebras and 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.- 6.5.1 Propositional Logic.- 6.5.2 Boolean Information Algebras.- 6.5.3 Linear Equations.- 6.5.4 Linear Inequalities.- 6.6 Compact Systems.- 6.7 Mappings.- 7 Uncertain Information.- 7.1 Algebra of Random Variables.- 7.1.1 Random Variables.- 7.1.2 Allocation of Probability.- 7.1.3 Support Functions.- 7.2 Probabilistic Argumentation Systems.- 7.2.1 Assumption-Based Information.- 7.2.2 Probabilistic Argumentation Systems.- 7.2.3 Operations with Argumentation Systems.- 7.3 Allocations of Probability.- 7.3.1 Algebra of Allocations.- 7.3.2 Normalized Allocations.- 7.3.3 Random Variables and Allocations.- 7.3.4 Labeled Allocations and their Algebra.- 7.4 Independent Sources.- 7.4.1 Independent Random Variables.- 7.4.2 Algebra of Bpas.- References.

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