Exercise 4.18 Naive Bayes with mixed features Consider a 3 class naive Bayes classifier with one binary feature and one Gaussian feature:

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|π, 1), x1|y = c ∼ Ber(x1|θc), x2|y = c ∼ N(x2|μc, σ2

c ) (4.283)

Let the parameter vectors be as follows:

π = (0.5, 0.25, 0.25), θ = (0.5, 0.5, 0.5), μ = (−1, 0, 1), σ2 = (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