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Page 4 of S Exercise 2. Weather Prediction Using Bayes Classifier 15 marks Imagine that you are given the following set of training examples. Training Data Play Tennis No Outlookk Temperature Humadity Wind Day 1 85 80 Day 4 Day 5 Day 6 Da Day 8 Day 9 Day 10 Day 11 Sun Sunn Overcast Rain Rain Rain Overcast Sunn Sun Rain Sunn Overcast Overcast Rain Weak Stron Weak Weak Weak Stron Stron Weak Weak Weak Stron Stron Weak Stron 68 65 80 65 95 72 60 75 75 Day 13 Day 14 81 No Assume that you have been given the following test data Test data Wind Weak Stron Strom Weak Stron Tennis Outlook Rain Ovecast Sun Overcast Rain Temperature Humidit 68 85 Yes 80 Tasks a) b) c) Discuss and comment on the results Classify the above test data using the Bayes Classifier model. each test case separately Develop a confusion matrix and calculate the accuracy and error rate of the NB classifier Show the calculations for

Answer 1

a) Sine we have 4 attributes we need to find probability of the game tennis played based on each attribute. So for aech attribute a table is to be constructed. Also from the data there are 5 cases where game can't be played and 9 cases where the game can be played.

OUTLOOK	Play=Yes	Play=No	Total
Sunny	2/9	3/5	5/14
Overcast	4/9	0/5	4/14
Rain	3/9	2/5	5/14

Since temperature is numeric values we need to deiscretize it as High,Medium,Low such that

temp 60-70 low

temp 70-80 medium

temp 80-90 high

TEMPERATURE	Play=Yes	Play=No	Total
Low	3/9	1/5	4/14
Medium	4/9	2/5	6/14
High	2/9	2/5	4/14

The same thing nedd to do in th case of humidity

humidity 60-70 Low4/

humdity 70-80 Medium

humidity 80 above High

HUMIDITY	Play=Yes	Play=No	Total
Low	1/9	0/5	1/14
Medium	4/9	1/5	5/14
High	4/9	4/5	8/14

WIND	Play=Yes	Play=No	Total
Weak	6/9	2/5	8/14
Strong	3/9	3/5	6/14

Also P(Play=Yes)=9/14 and P(play=No)=5/14

Now we have gathered all information for the calssifier.In the next step we can test it using test cases

1. X = (Outlook=Rain, Temperature=Low, Humidity=High, Wind=Weak)

from the table

• P(Outlook=Rain| Play=Yes) = 3/9
• P(Temperature=Low | Play=Yes) = 3/9
• P(Humidity=High | Play=Yes) = 4/9
• P(Wind=Weak| Play=Yes) = 6/9
• P(Play=Yes) = 9/14

Next we consider the fact that we cannot play a game:

• P(Outlook=Rain| Play=No) = 2/5
• P(Temperature=Low | Play=No) = 1/5
• P(Humidity=High | Play=No) = 4/5
• P(Wind=Weak| Play=No) = 2/5
• P(Play=No) = 5/14

P(X|Play=Yes)P(Play=Yes) =(3/9) * (3/9) * (4/9) * (6/9) * (9/14) = 0.0211

P(X|Play=No)P(Play=No) = (2/5) * (1/5) * (4/5) * (2/5) * (5/14) = 0.0091

Finally, we have to divide both results by the evidence

• P(X) = P(Outlook=Rain) * P(Temperature=Low) * P(Humidity=High) * P(Wind=Weak)
• P(X) = 5/14*4/14*8/14*8/14=0.033

Then, dividing the results by this value

§ P(Play=Yes | X) = 0.0211/0.033 = 0.6393

§ P(Play=No | X) = 0.0091/0.033= 0.2757

Since Play=Yes has the highest value we can play tennis in this case