GATE DA 2024 Set 1 — Question 62
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Machine Learning → Decision Trees & Ensembling → Information Gain
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Question
Details of ten international cricket games between two teams "Green" and "Blue" are given in Table C. This table consists of matches played on different pitches, across formats along with their winners. The attribute Pitch can take one of two values: spin-friendly (represented as ) or pace-friendly (represented as ). The attribute Format can take one of two values: one-day match (represented as ) or test match (represented as ).A cricket organization would like to use the information given in Table C to develop a decision-tree model to predict outcomes of future games between these two teams.To develop such a model, the computed InformationGain(C, Pitch) with respect to the Target is ______ (rounded off to two decimal places).Table C
| Match Number | Pitch | Format | Winner (Target) |
|---|---|---|---|
| 1 | Green | ||
| 2 | Blue | ||
| 3 | Blue | ||
| 4 | Blue | ||
| 5 | Green | ||
| 6 | Blue | ||
| 7 | Green | ||
| 8 | Blue | ||
| 9 | Blue | ||
| 10 | Green |
Correct answer
0.12 to 0.13
Solution
To calculate the Information Gain, we first compute the entropy of the Target (Winner) and then the conditional entropy of the Target given the attribute Pitch.1. Entropy of the Target (Parent Node):
From Table C, there are 10 matches in total.
2. Entropy of Target given Pitch:
We split the dataset based on Pitch values: and .For Pitch = S (5 matches):
Rounded to two decimal places, the Information Gain is 0.12.
From Table C, there are 10 matches in total.
- Green wins: Matches 1, 5, 7, 10 (Total = 4)
- Blue wins: Matches 2, 3, 4, 6, 8, 9 (Total = 6)
2. Entropy of Target given Pitch:
We split the dataset based on Pitch values: and .For Pitch = S (5 matches):
- Matches: 1, 2, 4, 7, 10
- Green wins: 1, 7, 10 (3 wins)
- Blue wins: 2, 4 (2 wins)
- ,
- Matches: 3, 5, 6, 8, 9
- Green wins: 5 (1 win)
- Blue wins: 3, 6, 8, 9 (4 wins)
- ,
Rounded to two decimal places, the Information Gain is 0.12.
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