Bayesian Belief Networks

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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.

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• 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.

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Conditional Probabilities in BBN

• This is actually the conditional probability of
  the variable 'Norman late' given the variable
  'train strike'.

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Entering hard evidence this is the simple
case. What about belief update in the other
direction?
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Entering hard evidence Note that our belief in
Martin being late is also increased. How does
evidence propagate in Belief Networks?
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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.
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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)
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Diverging connection ex2 entering some
evidence (hard or soft) about MartinLate is
propagated to TrainStrike, Oversleep and
NormanLate.
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Converging connection entering some evidence
(hard or soft) about MartinLate is propagated to
TrainStrike and Oversleep.
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Converging connection If we have no info about
MartinLate, Oversleep and TrainStrike is
independent no evidence is transmitted between
them.
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• Serial connection

What about the other direction? (we have some
evidence about C)?
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• Study from lecture notes in Bayesian Belief
  Nets.doc