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Review

THE HONG KONG UNIVERSITY OF SCIENCE & TECHNOLOGY CSIT 5220:  Reasoning and Decision under Uncertainty. Review. Overview. Bayesian networks Tool for applying probability theory to complex domains

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Review

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  1. THE HONG KONG UNIVERSITY OF SCIENCE & TECHNOLOGYCSIT 5220:  Reasoning and Decision under Uncertainty Review

  2. Overview • Bayesian networks • Tool for applying probability theory to complex domains • The concept: Joint Distribution, Chain rule, conditional independence, factorization  Bayesian network • D-separation, model building, inference, parameter learning, structure learning • Influence diagrams • Tool for applying normative decision theory to complex domains • The concept: BN + decision/utility nodes • Solution techniques: Decision trees, variable elimination

  3. Overview • Systematic study of general concepts/ideas in Probability/Decision Theory and Statistics • Random experiment, sample space, event, probability measure, probability weight function, frequentist/Bayesian interpretations • Random variable, probability mass function • Joint distribution, marginal distribution, independence, conditional independence, chain rule, noisy-OR • Prior/Posterior probability, likelihood, Bayes rule • Maximum likelihood estimation, EM algorithm, Bayesian estimation, Beta Distribution, conjugate families • Model selection, maximized likelihood, Bayesian information criteria • Decision theory, MEU principle, risk-seeking/aversion utilities, Decision trees • Naïve Bayes models, Gaussian mixture models, latent class models

  4. Page 4 Review • HW1 • Basics of Multivariate Probability and Bayesian networks • HW2 • Inference in Bayesian networks • HW3 • Learning with Bayesian networks • HW4 • Decision Making/Clustering • Plan • Go through the questionsone by one.

  5. HW1: Q1

  6. HW1, Q3 Analysis of Explaining away Page 6

  7. HW1, Q4 Page 7

  8. HW1, Q4 Page 8

  9. HW2, Q1, Q2 Page 9

  10. HW2, Q1, Q2 Key idea of BN • Factorization leads to efficient inference Page 10

  11. HW2, Q3 Page 11

  12. HW2, Q3 Page 12

  13. HW2, Q3 What if break ties alphabetically? Page 13

  14. HW2, Q3 Page 14

  15. HW2, Q4 Clique tree propagation Page 15

  16. Review Page 17 • HW1 • Basics of Multivariate Probability and Bayesian networks • HW2 • Inference in Bayesian networks • HW3 • Learning with Bayesian networks • HW4 • Decision Making

  17. HW3, Q1: EM Page 18

  18. Parameter Estimation Complete Data Page 19

  19. Parameter Estimation/Incomplete Data Idea of EM Page 20 Question on this idea

  20. Parameter Estimation/Incomplete Data The EM Algorithm Page 21

  21. HW3, Q2 Page 22

  22. Model Selection Page 23 Maximized likelihood does not work • Lead to overfitting, i.e., very complexity model structure

  23. Page 24

  24. Number of Parameters in BN Number of free parameters Page 25

  25. HW3, Q3 Page 26

  26. Constraint-Based Structure Learning The PC algorithm • Determine Skeleton • Set edge direction Page 27

  27. Review Page 28 • HW1 • Basics of Multivariate Probability and Bayesian networks • HW2 • Inference in Bayesian networks • HW3 • Learning with Bayesian networks • HW4 • Decision Making

  28. HW4, Q1 Page 29

  29. Decision Trees Classical way to represent decision problems with multiple decisions Explicitly show all possible sequences of decisions and observations. Page 30

  30. Average-Out and Folding-Back Page 31

  31. Influence Diagram A DAG with three types of nodes • Chance nodes, decision nodes, and utility nodes There is a directed path containing all the decision nodes. The utility nodes have no children. Each chance node is associated with the conditional distribution given its parents. Each utility node is associated with a utility function, a real-valued function of its parents. Page 32

  32. Influence Diagram and Decision Tree Page 33 How to convert influence diagram into decision tree • Draw tree • Root: the thing that happens first • Children of root: the thing that happens next • … • Figure out numerical information • Another algorithm: • Variable Elimination

  33. Page 34 Variable Elimination for Influence Diagram • Two set of potentials (factors): • Eliminate decision and chance nodes one by one according to a strong elimination ordering. • When eliminate variable X

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