Bayesian Networks: Representing Knowledge in an Uncertain Domain
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Presentation Transcript
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
