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Uncertainty

Probabilities and Belief Networks. Uncertainty. Burglary. Earthquake. P(B)=.001. P(E)=.002. B E | P(A) T T | .95 T F | .94 F T | .29 F F | .001. Alarm. JohnCalls. A | P(J) T | .90 F | .05. A | P(M) T | .70 F | .01. MaryCalls.

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Uncertainty

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  1. Probabilities and Belief Networks Uncertainty

  2. Burglary Earthquake P(B)=.001 P(E)=.002 B E | P(A) T T | .95 T F | .94 F T | .29 F F | .001 Alarm JohnCalls A | P(J) T | .90 F | .05 A | P(M) T | .70 F | .01 MaryCalls Note: < k+1 parents => O(dkn) numbers vs. O(dn)

  3. U1 Um x z1j znj Y1 Yn

  4. Three Ways in Which a Path can be blocked X E Y z (1) z (2) z (3)

  5. Computation in a BN • P(J|B) = • P(M|E,-B) = • P(B|J,-M) = • P(M,-J|B) = • P(-J,-M,B,E) =

  6. Representation of CPTs CH 14.3

  7. discrete • Canonical distribution: standard • Deterministic nodes: values computable exactly from parent nodes • Noisy-OR relations: Fever = Cold OR Flu OR Malaria OR leak-node • Leak node: covers anything else

  8. Continuous random variables • Discretization: large & inexact • Mixture of parametrized standard PDFs (e.g. Gaussians with mean & variance) • Hybrid Bayesian Networks: • BN with both discrete and continuous vars • E.g.: P(Buys|Cost), P(Cost|Harvest_quantity,Subsidy_boolean) • Use 2 linear gaussian PDF, one for Subsidy , one for not Subsidy • Can use multivariate Gaussian distributions • Conditional Gaussian: has Boolean parents • Probit distribution: Integral of a Gaussian up to x • A threshold affected by random Gaussian noise • Logit distribution: based on the sigmoid function: • E.g., P(buys | c)=1/(1+exp(-2(-c+mean)/sigma))

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