Bayesian Networks

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  “directly influences”)
• a conditional distribution for each node given its parents:

P(Xi|Parents(Xi))
In the simplest case, conditional distribution represented as a conditional probability table (CPT) giving the distribution over Xi for each combination of parent values

Example: Topology of network encodes conditional independence assertions:

Weather is independent of the other variables
Toothache and Catch are conditionally independent given Cavity

Example: I’m at work, neighbor John calls to say my alarm is ringing, but neighbor Mary doesn’t call. Sometimes it’s set off by minor earthquakes. Is there a burglar?
Variables: Burglar, Earthquake, Alarm, JohnCalls, MaryCalls Network topology reflects “causal” knowledge:

• A burglar can set the alarm off
• An earthquake can set the alarm off
• The alarm can cause Mary to call
• The alarm can cause John to call