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Q1) Naive Bayes Classifier: A village contains adults or kid, and each person has two features namely (height,weight). The model information is given by P (kid), P (adult) and p(xjkid) and p(xjadult) where x=(x(1), x(2))=(height,weight). Class conditionals i.e., are given by

 p(xjkid) = p 1 e ( 1 ( x(1) 1(1) ) 2 ) p 1 e ( 1 ( x(2) 1(2) ) 2 ) (1) 2 1(1) 2 1(2) 2 1 (1) 2 1(2) p(xjadult) = p 1 e ( 1 ( x(1) 2(1) ) 2 ) p 1 e ( 1 ( x(2) 2(2) ) 2 ); (2) 2 2(1) 2 2(2) 2 2 (1) 2 2(2)

where 1(1) = 1(2) = 2(1) = 2(2) = 1:0

a) Generate a population of size n = 1000. Show the two cluster of points. [25 Marks]

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b) Now use the points generated in the previous question to estimate P and p^. [15 Marks]

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c) Implement Baye’s rule using P and p^ [10 Marks]

Q2) Perceptron: Consider the same village problem as in previous exercise. However, now, the class conditionals i.e., are given by uniform distributions: the height for kids is distributed uniformly between [4:9; 5:3], the height of adult is distributed uniformly between [5:4; 5:9], the weight of kids is distributed uniformly between [30; 45] kilograms, and adults weight is distributed uniformly between [50; 65] kilograms.

1. Generate a population of size n = 1000. Show the two cluster of points. [10 Marks]

1. Use perceptron algorithm, and compute the decision rule. Show the decision boundary at each time instant [10 Marks]

Q3) Support Vector Machine: For the set of points generated in the preceptron example, show the classifier learnt by SVM [20 Marks]