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Bayesian Networks and Decision Graphs

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ISBN-10: 0387682813

ISBN-13: 9780387682815

Edition: 2nd 2007 (Revised)

Authors: Finn V. Jensen, Thomas D. Nielsen

List price: $129.99
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Probabilistic graphical models and decision graphs are powerful modeling tools for reasoning and decision making under uncertainty. As modeling languages they allow a natural specification of problem domains with inherent uncertainty, and from a computational perspective they support efficient algorithms for automatic construction and query answering. This includes belief updating, finding the most probable explanation for the observed evidence, detecting conflicts in the evidence entered into the network, determining optimal strategies, analyzing for relevance, and performing sensitivity analysis. The book introduces probabilistic graphical models and decision graphs, including Bayesian…    
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Book details

List price: $129.99
Edition: 2nd
Copyright year: 2007
Publisher: Springer New York
Publication date: 6/6/2007
Binding: Hardcover
Pages: 447
Size: 6.10" wide x 9.25" long x 0.75" tall
Weight: 1.694
Language: English

Prerequisites on Probability Theory
Two Perspectives on Probability Theory
Fundamentals of Probability Theory
Conditional Probabilities
Probability Calculus
Conditional Independence
Probability Calculus for Variables
Calculations with Probability Tables: An Example
An Algebra of Potentials
Random Variables
Continuous Distributions
Probabilistic Graphical Models
Causal and Bayesian Networks
Reasoning Under Uncertainty
Car Start Problem
A Causal Perspective on the Car Start Problem
Causal Networks and d-Separation
Bayesian Networks
Definition of Bayesian Networks
The Chain Rule for Bayesian Networks
Inserting Evidence
Calculating Probabilities in Practice
Graphical Models - Formal Languages for Model Specification
Bibliographical Notes
Building Models
Catching the Structure
Milk Test
Cold or Angina?
A Simplified Poker Game
Naive Bayes Models
Determining the Conditional Probabilities
Milk Test
Stud Farm
Poker Game
Transmission of Symbol Strings
Cold or Angina?
Why Causal Networks?
Modeling Methods
Undirected Relations
Noisy Functional Dependence
Expert Disagreements
Object-Oriented Bayesian Networks
Dynamic Bayesian Networks
How to Deal with Continuous Variables
Special Features
Joint Probability Tables
Most-Probable Explanation
Data Conflict
Sensitivity Analysis
Bibliographical Notes
Belief Updating in Bayesian Networks
Introductory Examples
A Single Marginal
Different Evidence Scenarios
All Marginals
Graph-Theoretic Representation
Task and Notation
Domain Graphs
Triangulated Graphs and Join Trees
Join Trees
Propagation in Junction Trees
Lazy Propagation in Junction Trees
Exploiting the Information Scenario
Barren Nodes
Nontriangulated Domain Graphs
Triangulation of Graphs
Triangulation of Dynamic Bayesian Networks
Exact Propagation with Bounded Space
Recursive Conditioning
Stochastic Simulation in Bayesian Networks
Probabilistic Logic Sampling
Likelihood Weighting
Gibbs Sampling
Loopy Belief Propagation
Bibliographical Notes
Analysis Tools for Bayesian Networks
IEJ Trees
Joint Probabilities and A-Saturated Junction Trees
A-Saturated Junction Trees
Configuration of Maximal Probability
Axioms for Propagation in Junction Trees
Data Conflict
The Conflict Measure conf
Conflict or Rare Case
Tracing of Conflicts
Other Approaches to Conflict Detection
SE Analysis
Example and Definitions
h-Saturated Junction Trees and SE Analysis
Sensitivity to Parameters
One-Way Sensitivity Analysis
Two-Way Sensitivity Analysis
Bibliographical Notes
Parameter Estimation
Complete Data
Maximum Likelihood Estimation
Bayesian Estimation
Incomplete Data
Approximate Parameter Estimation: The EM Algorithm
Why We Cannot Perform Exact Parameter Estimation
Fractional Updating
Specification of an Initial Sample Size
Example: Strings of Symbols
Adaptation to Structure
Fractional Updating as an Approximation
Determining grad dist(x, y) as a Function of t
Bibliographical Notes
Learning the Structure of Bayesian Networks
Constraint-Based Learning Methods
From Skeleton to DAG
From Independence Tests to Skeleton
Constraint-Based Learning on Data Sets
Ockham's Razor
Score-Based Learning
Score Functions
Search Procedures
Chow-Liu Trees
Bayesian Score Functions
Bibliographical Notes
Bayesian Networks as Classifiers
Naive Bayes Classifiers
Evaluation of Classifiers
Extensions of Naive Bayes Classifiers
Classification Trees
Bibliographical Notes
Decision Graphs
Graphical Languages for Specification of Decision Problems
One-Shot Decision Problems
Fold or Call?
One Decision in General
Instrumental Rationality
Decision Trees
A Couple of Examples
Coalesced Decision Trees
Solving Decision Trees
Influence Diagrams
Extended Poker Model
Definition of Influence Diagrams
Repetitive Decision Problems
Asymmetric Decision Problems
Different Sources of Asymmetry
Unconstrained Influence Diagrams
Sequential Influence Diagrams
Decision Problems with Unbounded Time Horizons
Markov Decision Processes
Partially Observable Markov Decision Processes
Bibliographical Notes
Solution Methods for Decision Graphs
Solutions to Influence Diagrams
The Chain Rule for Influence Diagrams
Strategies and Expected Utilities
An Example
Variable Elimination
Strong Junction Trees
Required Past
Policy Networks
Node Removal and Arc Reversal
Node Removal
Arc Reversal
An Example
Solutions to Unconstrained Influence Diagrams
Minimizing the S-DAG
Determining Policies and Step Functions
Decision Problems Without a Temporal Ordering: Troubleshooting
Action Sequences
A Greedy Approach
Call Service
Solutions to Decision Problems with Unbounded Time Horizon
A Basic Solution
Value Iteration
Policy Iteration
Solving Partially Observable Markov Decision Processes
Limited Memory Influence Diagrams
Bibliographical Notes
Methods for Analyzing Decision Problems
Value of Information
Test for Infected Milk?
Myopic Hypothesis-Driven Data Request
Non-Utility-Based Value Functions
Finding the Relevant Past and Future of a Decision Problem
Identifying the Required Past
Sensitivity Analysis
One-Way Sensitivity Analysis in General
Bibliographical Notes
List of Notation