Question

For this problem, use the e1-p3.csv dataset.

A1	A2	A3	Class
low	hot	medium	Y
low	mild	large	N
low	hot	small	N
low	cold	medium	N
high	cold	small	N
high	mild	medium	Y
high	cold	large	N
low	cold	medium	Y
high	mild	large	Y
low	mild	large	N
high	hot	medium	Y
high	cold	large	N
low	mild	small	Y
low	hot	small	N
low	hot	medium	N

(1). Using the Naïve Bayes algorithm that we discussed in the class, classify the following unseen instance:

            X = <A1 = high, A2 = hot, A3 = large>

You should not use Weka, JMP Pro, or any other data mining/machine learning software. You must show all intermediate results and calculations.

(2). Suppose that P(X) = 0.0667. Calculate P(Y | X) and P(N | X). You must show all intermediate results and calculations.

Answer 1

Hi,

First we should know the formula

Naive assumption : if any two events A and B and they are independent, then

P(A,B) = P(A) P(B)

Based on classes, we calculate the all conditional probabilties

Now, we pick up the output with maximum probability and which gives label of class and can be expressed as given below.

now comes to our question

In the above image, we are able to see that P(X|Y) has less probability than P(X|N) so P(X|N) will dominate P(X|Y)hence X intance will be labeled as "NO" .

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Hope it helps..

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Thank You !