Aritificial Intelligence Lab 5 Solution

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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.

  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]