Question

Sunny	true	None	Play
rain	True	Slight	Stay Home
overcast	false	slight	Play
rain	false	heavy	Stay Home
Sunny	true	none	Play
overcast	false	slight	Play

a. Using the above datasets, calculate the Prior probabilities for each class label. Clearly show your calculations.

b. Calculate the Conditional Probabilities for All attributes. Clearly show your calculations.

c. What is the most likely classification using Naïve Bayes Algorithm for the following unseen instance (show your calculations):

overcast

true

heavy

??????

Question 2:   ​​​​​   [10 Marks]

• Consider the following dataset:

(a) Based on the nearest neighbors with 2D graph, what is the classification for the following unseen attributes using K nearest neighbors (K=3), show the calculation within X Y Graph?

instance 6

3.2

5.4

??

Instances	Attribute 1	Attribute 2	Class
instance 1	0.8	6.3	Positive
instance 2	1.4	8.1	Negative
instance 3	1.2	7.4	Positive
instance 4	6.2	14.3	Positive
instance 5	6.8	11.6	Negative

Answer 1

Question 1

(a) Prior Probabilities of each Class Label:

Stay Home = 2/6 = 0.3334

Play = 4/6 = 0.6667

(b) Conditional Probabilities for each attributes are:

Outlook (X1)	P(X1/Y=Play)	P(X1/Y=Stay Home)
Sunny	2/4	0/2
Rain	0/4	2/2
Overcast	2/4	0/2
Windy (X2)	P(X2/Y=Play)	P(X2/Y=Stay Home)
True	2/4	1/2
False	2/4	1/2
Rain (X3)	P(X3/Y=Play)	P(X3/Y=Stay Home)
None	2/4	0/2
Slight	2/4	1/2
Heavy	0/4	1/2

(c) Predicting using Naive Bayes

X1 = Overcast, X2 = True and X3 = Heavy

P(Play/X) = 2/4 * 2/4 * 0/4 * 4/6 = 0

P(Stay Home/X) = 0/2 * 1/2 * 1/2 * 2/6 = 0

In order to calculate any legitimate value to probability, adding 0.01 to both the probabilities result to smoothen the function value.

P(Play/X) = 0.01

P(Stay Home/X) = 0.01

As P(Play/X) + P(Stay Home/X) = 1

Hence, converting these numbers to make sum = 1

P(Play/X) = 0.5 and

P(Stay Home/X) = 0.5

Both the probabilities are same, and hence

(i) As the prior probability of Playing is >= 0.667, hence

Then it will be classified into Stay Home as p < 0.667

Question 2

From the above graph the three nearest neighbors of unseen attribute are (0.8 , 6.3), (1.4 , 8.1), (1.2 , 7.4)

out of which 2 is postive and 1 is negative..

So the unseen attribute is classified as positive.