1. Chapter 14
February 26, 2004

2. 14.1 Representing Knowledge in an Uncertain Domain
Bayesian Networks
random variables
directed links (X influences Y)
conditional probability tables
directed, acyclic graph
Example: Figure 14.1
Example: Figure 14.2

3. 14.2 The Semantics of Bayesian Networks
Determining the full joint distribution
P(j  m  a  ¬b  ¬e) = P(j | a) * P(m | a) * P(a| ¬ b  ¬ e) * P(¬ b) * P(¬ e)
P(x1, x2, x3) = P(x3 | x1, x2) * P(x1, x2)
P(x1, x2) = P(x2 | x1) * P(x1)

4. Bayesian Networks can be compact
n Boolean random variables
k upper bound on incoming arrows
2n vs n*2k probabilities needed

5. Network structure depends on order of introduction
Figure 14.3
Causal models are typically better than diagnostic models

6. Conditional independence relations in Bayesian Networks
Figure 14.4

7. 14.3 Efficient Representation of Conditional Distributions
Noisy-Or, p. 501
Hybrid Bayesian Network (Figures )
discrete  discrete
discrete  continuous
continuous  discrete
continuous  continuous

8. 14.4 Exact Inference in Bayesian Networks
The section describes tricks to do the inference more efficiently.
Clustering, Figure 14.11
Goal is to produce a polytree
Often used in commercial Bayesian systems
No magic bullet

9. Midterm Review Thursday, March 4th Open book, open notes, etc.
Bring a calculator
Major topics are …

10. 9: Inference in First-Order Logic
Unification
Forward Chaining
Backward Chaining
Prolog
Resolution Theorem Proving
Resolution Strategies

11. 10: Knowledge Representation
Ontologies
Situation Calculus
Intervals
Frame Problem
Semantic Networks
Closed World Assumption
Unique Names Assumption

12. 18: Learning from Observations
Decision Trees
Ensemble Learning / AdaBoost
PAC learning

13. 19: Knowledge in Learning
Version Space
Explanation Based Learning

14. 20: Statistical Learning Methods
Maximum-likelihood parameter learning: discrete models
Naive Bayes models
K nearest neighbors
Perceptrons
Backpropagation Neural Networks

15. 13: Uncertainty Terminology Conditional Probability
Axioms of Probability
Inference Using Full Joint Distributions
Independence
Baye’s Rule

16. 14: Probabilistic Reasoning
Bayesian Networks
Construction
Reasoning With