What is the difference between a Bayesian network and a naive Bayes classifier?

Question

What is the difference between a Bayesian network and a Naive Bayes classifier? I noticed one is just implemented in Matlab as classify the other has an entire

Answer 1

Naive Bayes is just a restricted/constrained form of a general Bayesian network where you enforce the constraint that the class node should have no parents and that the nodes corresponding to the attribute variables should have no edges between them. As such, there is nothing that prevents a general Bayesian network from being used for classification - the predicted class is the one with the maximum probability when (conditioned on) all the other variables are set to the prediction instance values in the usual Bayesian inference fashion. A good paper to read on this is "Bayesian Network Classifiers, Machine Learning, 29, 131–163 (1997)". Of particular interest is section 3. Though Naive Bayes is a constrained form of a more general Bayesian network, this paper also talks about why Naive Bayes can and does outperform a general Bayesian network in classification tasks.