Learning a Bayes classifier without independence assumptions requires an unrealistic number of training examples.
Compute the number of parameters to be learned for a model Y = f(X) where Y is a boolean variable,
and X is vector of N boolean features.
What is the number of parameters under Naive Bayes assumptions?
p(Y | X) = p(X | Y) p(Y) / p(X)
Number of parameters for p(Y)
Number of parameters for p(X | Y)
Number of parameters under Naive Bayes independence assumption: