A Probabilistic Generative Model For Classification Comprises Class Conditional Densities Plyck And Class Priors P Cx 1 (46.74 KiB) Viewed 24 times
A Probabilistic Generative Model For Classification Comprises Class Conditional Densities Plyck And Class Priors P Cx 2 (50.34 KiB) Viewed 24 times
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-
1. (20 points) Maximum likelihood (ML) parameter estimation In class, we derived the ML parameters for model i): Nk PCk) - Nk N де ΑΣ, ΣΧ K Σ = N k=1 Sk NECR where 1 Sk = (xn – Hx)(xn – MX)", NE NECA Ng is the number of data points in class Ck, and N is the total number of data points in the data set. (a) (10 points) Find the ML parameters for model ii), i.e., find: P(C), HDR (Hint: You should incorporate a Lagrange multiplier that El P(Ck) = 1.) (b) (10 points) Find the ML parameters for model iii), i.e., find: P(Ck), Aki
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