Summary Bayesian Belief Network

Bayesian Belief Network




P(a ! b) = P(a ) P(b)
P(toothache, catch, cavity, Weather = cloudy ) =
= P(Weather = cloudy ) P(toothache, catch, cavity )

• The decomposition of large probabilistic domains into
weakly connected subsets via conditional
independence is one of the most important
developments in the recent history of AI

• This can work well, even the assumption is not true!




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,vNB

 Naive Bayes assumption:



 which gives




 Bayesian networks
 Conditional Independence
 Inference in Bayesian Networks
 Irrelevant variables
 Constructing Bayesian Networks
 Aprendizagem Redes Bayesianas

 Examples - Exercisos




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,  Naive Bayes assumption of conditional
independence too restrictive
 But it's intractable without some such
assumptions...

 Bayesian Belief networks describe conditional
independence among subsets of variables
 allows combining prior knowledge about
(in)dependencies among
variables with observed training data




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




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