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Bayesian Belief Networks
• A BBN is a directed, acyclic graph together with an associated
set of probability tables. The graph consists of nodes and arcs.
• The nodes represent random variables which can be discrete or
continuous. For example, a node might represent the variable 'Train strike' which is
discrete, having the two possible values 'true' and 'false'.
• The arcs can be thought as causal relationships between
variables, but in general,
an arc from X to Y means
“X has direct influence” on our belief in Y.
• The key feature of BBNs is that they enable us to model
and reason about uncertainty.
– In our example, a train strike does not imply that Norman will
definitely be late (he might leave early and drive), but there is
an increased probability that he will be late.
– In the BBN we model this by filling in a conditional
probability table for each node.
Conditional Probabilities in BBN
• This is actually the
conditional probability of the
variable 'Norman late' given
the variable 'train strike'.
Entering hard evidence: this is the simple case.
What about belief update in the other direction?
Entering hard evidence
Note that our belief in Martin being late is also increased. How does
evidence propagate in Belief Networks?
Diverging connection: entering some evidence (hard or soft) about
NormanLate is propagated to TrainStrike and MartinLate.
If we had hard evidence about TrainStrike, any new evidence about
NormanLate would not be propagated to MartinLate.
Diverging connection: If we had hard evidence about TrainStrike, any new
evidence about NormanLate would not be propagated to MartinLate (the
chidren are then conditionally independent given the parent)
Diverging connection – ex2: entering some evidence (hard or soft) about
MartinLate is propagated to TrainStrike, Oversleep and NormanLate.
Converging connection: entering some evidence (hard or soft) about
MartinLate is propagated to TrainStrike and Oversleep.
Converging connection: If we have no info about MartinLate, Oversleep
and TrainStrike is independent: no evidence is transmitted between them.
• Serial connection:
What about the other direction? (we have some evidence about C)?
• Study from lecture notes in Bayesian Belief Nets.doc