Solved–Aritificial Intelligence Lab 5– Solution

Description

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]

2. 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]