Consider a Naive Bayes classifier for a binary classification task in a two-dimensional feature space with...

 

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Consider a Naive Bayes classifier for a binary classification task in a two-dimensional feature space with P(x|C) ~ G(,), P(xC) G (2.2) and P(C) = P(C) = 1, where x = is a sample observation, ; is the 2 1 mean vector for class C; and , is the 2 x2 covariance matrix for class C. x2 Let g(x)=In(P(x|C)P(C)) be the discriminant function for class C. Then, let g(x) = g (x)-g2(x). Using the Bayesian decision theory we find: 1. (4 points) Let = M2 = and = 0 Choose C if g(x) > 0 Choose Co otherwise 2 = I. Find g(x) and show all your work. What is the shape of the decision boundary?. 2. (4 points) Let = H 0.5 5 and 2 = .Find g(x) and show all your work. What is the shape of the 0.5 2 4 5 decision boundary?. Consider a Naive Bayes classifier for a binary classification task in a two-dimensional feature space with P(x|C) ~ G(,), P(xC) G (2.2) and P(C) = P(C) = 1, where x = is a sample observation, ; is the 2 1 mean vector for class C; and , is the 2 x2 covariance matrix for class C. x2 Let g(x)=In(P(x|C)P(C)) be the discriminant function for class C. Then, let g(x) = g (x)-g2(x). Using the Bayesian decision theory we find: 1. (4 points) Let = M2 = and = 0 Choose C if g(x) > 0 Choose Co otherwise 2 = I. Find g(x) and show all your work. What is the shape of the decision boundary?. 2. (4 points) Let = H 0.5 5 and 2 = .Find g(x) and show all your work. What is the shape of the 0.5 2 4 5 decision boundary?.

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