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

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

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]