Exercise 4.18 Naive Bayes with mixed features
Consider a 3 class naive Bayes classifier with one binary feature and one Gaussian feature:
y ? Mu(y|?, 1), x1|y = c ? Ber(x1|?c), x2|y = c ? N(x2|?c, ?2
c ) (4.283)
Let the parameter vectors be as follows:
? = (0.5, 0.25, 0.25), ? = (0.5, 0.5, 0.5), ? = (?1, 0, 1), ?2 = (1, 1, 1) (4.284)
a. Compute p(y|x1 = 0, x2 = 0) (the result should be a vector of 3 numbers that sums to 1).
b. Compute p(y|x1 = 0).
c. Compute p(y|x2 = 0).
d. Explain any interesting patterns you see in your results. Hint: look at the parameter vector
