Bayesian networksChapter 14.3Chapter 14.3 1Outline♦ Parameterized distributionsChapter 14.3 2Compact conditional distributionsCPT grows exponentially with number of parentsCPT becomes infinite with continuous-valued parent or childSolution:canonical distributions that are defined compactlyDeterministic nodes are the simplest case:X = f(P arents(X)) for some function fE.g., Boolean functionsNorthAmerican ⇔ Canadian ∨ US ∨ MexicanE.g., numerical relationships among continuous variables (parents=car prices,child=bargain price, f=min(car prices))Chapter 14.3 3Compact conditional distributions contd.Noisy-OR distributions model multiple noninteracting causes1) ParentsU1. . . Ukinclude all causes (can ad d leak node)2) Independent failure probabilityqifor each cause alone⇒ P (X|U1. . . Uj, ¬Uj+1. . . ¬Uk) = 1 − Πji = 1qiCold F lu Malaria P (F ever) P (¬F ever)F F F 0.0 1.0F F T 0.9 0.1F T F 0.8 0.2F T T 0.98 0.02 = 0.2 × 0.1T F F 0.4 0.6T F T 0.94 0.06 = 0.6 × 0.1T T F 0.88 0.12 = 0.6 × 0.2T T T 0.988 0.012 = 0.6 × 0.2 × 0.1Number of parameters linear in number of parentsChapter 14.3 4Hybrid (discrete+continuous) networksDiscrete (Subsidy? and Buys?); continuous (Harvest and Cost)Buys?HarvestSubsidy?CostOption 1: discretization—possibly large errors, large CPTsOption 2: finitely parameterized canonical families1) Continuous variable, discrete+continuous parents (e.g.,Cost)2) Discrete variable, continuous parents (e.g.,Buys?)Chapter 14.3 5SummaryCanonical distributions (e.g., noisy-OR) = compact r epresentation of CPTsContinuous variables ⇒ parameter ized distributions (e.g., linear Gaussian)Chapter 14.3
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