Chapter 14 February 26 2004 14 1 Representing

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(x 1, x 2, x 3) = P(x 3 | x 1, x 2) * P(x 1, x 2) • P(x 1, x 2) = P(x 2 | x 1) * P(x 1)

• Bayesian Networks can be compact • n Boolean random variables • k upper bound on incoming arrows • 2 n vs n*2 k 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. 514. 7) – discrete continuous – continuous discrete – 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 4 th • 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 / Ada. Boost • 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