4.9 ( ) www Consider a generative classification model for K classes defined by prior class probabilities p(Ck) = k and general class-conditional densities p(|Ck)

4.9 () www Consider a generative classification model for K classes defined by prior class probabilities p(Ck) = πk and general class-conditional densities p(φ|Ck)

where φ is the input feature vector. Suppose we are given a training data set {φn, tn}

where n = 1, . . . , N, and tn is a binary target vector of length K that uses the 1-of-

K coding scheme, so that it has components tnj = Ijk if pattern n is from class Ck.

Assuming that the data points are drawn independently from this model, show that the maximum-likelihood solution for the prior probabilities is given by

πk = Nk N

(4.159)

where Nk is the number of data points assigned to class Ck.