Working Group Neural Networks and Fuzzy Systems

Graphical Models

Table of Contents

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• 1 Introduction
  • 1.1 Data and Knowledge
  • 1.2 Knowledge Discovery and Data Mining
    • 1.2.1 The KDD Process
    • 1.2.2 Data Mining Tasks
    • 1.2.3 Data Mining Methods
  • 1.3 Graphical Models
  • 1.4 Outline of this Book
• 2 Imprecision and Uncertainty
  • 2.1 Modeling Inferences
  • 2.2 Imprecision and Relational Algebra
  • 2.3 Uncertainty and Probability Theory
  • 2.4 Possibility Theory and the Context Model
    • 2.4.1 Experiments with Dice
    • 2.4.2 The Context Model
    • 2.4.3 The Insufficient Reason Principle
    • 2.4.4 Overlapping Contexts
    • 2.4.5 Mathematical Formalization
    • 2.4.6 Normalization and Consistency
    • 2.4.7 Possibility Measures
    • 2.4.8 Mass Assignment Theory
    • 2.4.9 Degrees of Possibility for Decision Making
    • 2.4.10 Conditional Degrees of Possibility
    • 2.4.11 Imprecision and Uncertainty
    • 2.4.12 Open Problems
• 3 Decomposition
  • 3.1 Decomposition and Reasoning
  • 3.2 Relational Decomposition
  • 3.2.1 A Simple Example
  • 3.2.2 Reasoning in the Simple Example
  • 3.2.3 Decomposability of Relations
  • 3.2.4 Tuple-Based Formalization
  • 3.2.5 Possibility-Based Formalization
  • 3.2.6 Conditional Possibility and Independence
  • 3.3 Probabilistic Decomposition
  • 3.3.1 A Simple Example
  • 3.3.2 Reasoning in the Simple Example
  • 3.3.3 Factorization of Probability Distributions
  • 3.3.4 Conditional Probability and Independence
  • 3.4 Possibilistic Decomposition
  • 3.4.1 Transfer from Relational Decomposition
  • 3.4.2 A Simple Example
  • 3.4.3 Reasoning in the Simple Example
  • 3.4.4 Conditional Degrees of Possibility and Independence
  • 3.5 Possibility versus Probability
• 4 Graphical Representation
  • 4.1 Conditional Independence Graphs
    • 4.1.1 Axioms of Conditional Independence
    • 4.1.2 Graph Terminology
    • 4.1.3 Separation in Graphs
    • 4.1.4 Dependence and Independence Maps
    • 4.1.5 Markov Properties of Graphs
    • 4.1.6 Graphs and Decompositions
    • 4.1.7 Markov Networks and Bayesian Networks
  • 4.2 Evidence Propagation in Graphs
    • 4.2.1 Propagation in Polytrees
    • 4.2.2 Join Tree Propagation
    • 4.2.3 Other Evidence Propagation Methods
• 5 Computing Projections
  • 5.1 Databases of Sample Cases
  • 5.2 Relational and Sum Projections
  • 5.3 Expectation Maximization
  • 5.4 Maximum Projections
    • 5.4.1 A Simple Example
    • 5.4.2 Computation via the Support
    • 5.4.3 Computation via the Closure
    • 5.4.4 Experimental Results
    • 5.4.5 Limitations
• 6 Naive Classifiers
  • 6.1 Naive Bayes Classifiers
    • 6.1.1 The Basic Formula
    • 6.1.2 Relation to Bayesian Networks
    • 6.1.3 A Simple Example
  • 6.2 A Naive Possibilistic Classifier
  • 6.3 Classifier Simplification
  • 6.4 Experimental Results
• 7 Learning Global Structure
  • 7.1 Principles of Learning Global Structure
    • 7.1.1 Learning Relational Networks
    • 7.1.2 Learning Probabilistic Networks
    • 7.1.3 Learning Possibilistic Networks
    • 7.1.4 Components of a Learning Algorithm
  • 7.2 Evaluation Measures
    • 7.2.1 General Considerations
    • 7.2.2 Notation and Presuppositions
    • 7.2.3 Relational Evaluation Measures
    • 7.2.4 Probabilistic Evaluation Measures
    • 7.2.5 Possibilistic Evaluation Measures
  • 7.3 Search Methods
    • 7.3.1 Exhaustive Graph Search
    • 7.3.2 Guided Random Search
    • 7.3.3 Conditional Independence Search
    • 7.3.4 Greedy Search
  • 7.4 Experimental Results
    • 7.4.1 Learning Probabilistic Networks
    • 7.4.2 Learning Possibilistic Networks
• 8 Learning Local Structure
  • 8.1 Local Network Structure
  • 8.2 Learning Local Structure
  • 8.3 Experimental Results
• 9 Inductive Causation
  • 9.1 Correlation and Causation
  • 9.2 Causal and Probabilistic Structure
  • 9.3 Stability and Latent Variables
  • 9.4 The Inductive Causation Algorithm
  • 9.5 Critique of the Underlying Assumptions
  • 9.6 Evaluation
• 10 Applications
  • 10.1 Applications in Telecommunications
  • 10.2 Application at Volkswagen
  • 10.3 Application at DaimlerChrysler
• A Proofs of Theorems
• B Software Tools
• Bibliography
• Index

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