Answer Happy

A probabilistic generative model for classification comprises class-conditional densities PlyCk) and class priors P(Cx), where y ERP and k = 1, ...,K. We will consider three different generative models in this problem set: i) Gaussian, shared covariance y | Ce~ N(Hk, ) ii) Gaussian, class-specific covariance y | C, NN (μ., Σι) iii) Poisson yix Poisson (vi) In iii), yi is the ith element of the vector y, where i = 1,..., D. This is called a naive Bayes model, since the yi are independent conditioned on CR-

2. (20 points) Decision boundaries In class, we derived the decision boundary between class Ck and class C; for model i): (Wk – w;) x + (WKO – W;o) = 0, WRO where w, = Σ'με s- Hk + log PCk). -') For each of the models ii) and iii), we'll want to derive the decision boundary between class Ck and class C; and say whether it is linear in y. (a) (10 points) What is the decision boundary for model (ii)? Is it linear? (b) (10 points) What is the decision boundary for model (iii)? Is it linear?