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(x|kid) and p(x|adult) where x=(x(1), x(2))=(height,weight). Class conditionals i.e., are given by
where σ1 (1) = σ1 (2) = σ2 (1) = σ2 (2) = 1.0
a) Generate a population of size n = 1000. Show the two cluster of points. [25 Marks]
b) Now use the points generated in the previous question to estimate Pˆ and pˆ. [15 Marks]
c) Implement Baye’s rule using Pˆ and pˆ [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.
a) Generate a population of size n = 1000. Show the two cluster of points. [10 Marks]
b) 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]
