Exercise 2 E [4 points]. Given a training set D = {(x(i), y(i)), i = 1,...

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Exercise 2 E [4 points]. Given a training set D = {(x(i), y(i)), i = 1, .., M}, where x() RN and y() {1,2, ..., C}, derive the maximum likelihood estimates of the naive Bayes for real valued xmodeled with a Laplacian distribution, i.e., (-105 = Hsled). p(x, y = c) = 1 20j|c exp Exercise 3 [4 points]. Prove that in binary classification, the posterior of linear discrim- inant analysis, i.e., p(y = 1|x; y, , ), is in the form of a sigmoid function p(y = 1|x; 0) = 1 1+e-0x where is a function of {y, , }. Hint: remember to use the convention of letting to 1 that incorporates the bias term into the parameter vector 0. = 2 Exercise 2 E [4 points]. Given a training set D = {(x(i), y(i)), i = 1, .., M}, where x() RN and y() {1,2, ..., C}, derive the maximum likelihood estimates of the naive Bayes for real valued xmodeled with a Laplacian distribution, i.e., (-105 = Hsled). p(x, y = c) = 1 20j|c exp Exercise 3 [4 points]. Prove that in binary classification, the posterior of linear discrim- inant analysis, i.e., p(y = 1|x; y, , ), is in the form of a sigmoid function p(y = 1|x; 0) = 1 1+e-0x where is a function of {y, , }. Hint: remember to use the convention of letting to 1 that incorporates the bias term into the parameter vector 0. = 2

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Exercise 2 To derive the maximum likelihood estimates of the naive Bayes for realvalued data modeled with a Laplacian distribution we need to estimate ... View the full answer