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Understanding Probabilities and Belief Networks: Uncertainty in Burglary and Earthquake Scenarios

Learn about probabilities and belief networks in scenarios involving burglary and earthquakes. Explore different computations in Bayesian networks, representation of conditional probability tables, and handling discrete and continuous random variables.

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Understanding Probabilities and Belief Networks: Uncertainty in Burglary and Earthquake Scenarios

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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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