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A Bayesian classifier is based on the idea that the role of a (natural) class is to predict the values of features for members of that class. Examples are grouped in classes because they have common values for the features. Such classes are often called natural kinds. In this section, the target feature corresponds to a discrete class, which is not necessarily binary.  The idea behind a Bayesian classifier is that, if an agent knows the class, it can predict the values of the other features. If it does not know the class, Bayes' rule can be used to predict the class given (some of) the feature values. In a Bayesian classifier, the learning agent builds a probabilistic model of the features and uses that model to predict the classification of a new example.  Given an example with inputs X1=v1,...,Xk=vk, Bayes' rule is used to compute the posterior probability distribution of the example's classification, 
  Y:  \textbf{P(Y | X1=v1,...,Xk=vk)}  \textbf{= (P(X1=v1,...,Xk=vk| Y) ×P(Y))/(P(X1=v1,...,Xk=vk))}