BN1 - Bayesian networks A simple graphical notation for...

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Bayesian networks A simple, graphical notation for conditional independence assertions and hence for compact specification of full joint distributions Syntax A set of nodes, one per variable A directed, acyclic graph (link implies direct influence) A conditional distribution for each node given its parents Conditional distributions For each X i , P(X i |Parents(X i )) In the form of a conditional probability table (CPT) Distribution of X i for each combination of parent values
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Example Topology of network encodes conditional independence assertions Weather Cavity Toothache Catch Weather is independent of the other variables Toothache,Catch are conditionally independent given Cavity
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Example I’m at work, neighbor John calls to say my alarm is ringing, but neighbor Mary doesn’t call. Sometimes it’s set o by minor earthquakes. Is there a burglar? Variables: Burglar, Earthquake, Alarm, JohnCalls, MaryCalls Network topology reflects “causal” knowledge A burglar can set the alarm o An earthquake can set the alarm o The alarm can cause Mary to call The alarm can cause John to call
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Example (Contd.)
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