Chapter 14 February 26, 2004

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

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)

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

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

Conditional independence relations in Bayesian Networks Figure 14.4

14.3 Efficient Representation of Conditional Distributions Noisy-Or, p. 501 Hybrid Bayesian Network (Figures 14.5-14.7) discrete  discrete discrete  continuous continuous  discrete continuous  continuous

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

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

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

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

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

19: Knowledge in Learning Version Space Explanation Based Learning

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

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

14: Probabilistic Reasoning Bayesian Networks Construction Reasoning With