Consider the decision trees shown in Figure 1. The decision tree in 1b is a pruned version of the original decision tree 1a. The training and test sets are shown in table 5. For every combination of values for attributes A and B, we have the number of instances in our dataset that have a positive or negative label.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
Section: Chapter Questions
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3
Consider the decision trees shown in Figure 1. The decision tree in 1b is a pruned version of the original
decision tree 1a. The training and test sets are shown in table 5. For every combination of values for
attributes A and B, we have the number of instances in our dataset that have a positive or negative label.
0
3.1
+
0
3.4
B
0
0
0
1
1
0
1 1
~~
3.5
2 0
2 1
1
0
+
5
3
22
7
26
A
(a) Decision Tree 1 (DT1)
2
1
6
B
Training set
# of (+) instances #of (-)
1
0
34
3
4
7
32
54
2
5
instances
4
B
1
+
Figure 1
Table 5
+
4
0
36352
0
3
+
A
1
B
Test set
# of (+) instances # of (-) instances
3.3
Build the confusion matrices when using DT1 and DT2 to predict for the test set.
1
(b) Decision Tree 2 (DT2)
Estimate the generalization error rate of both trees shown in Figure 1 (DT1, DT2) using the optimistic
approach and the pessimistic approach. To account for model complexity with the pessimistic approach,
use a penalty value of 2 = 2 for each leaf node.
Compute the error rate of the DT1 and DT2 on the test set shown in the table 5.
3.2
Which tree would you select? In other words, would you use the original decision tree or would you prune
it? Briefly explain how you will decide.
2
1
1
3
15
25
Calculate the test accuracy, precision, recall, and F1-score of DT1 and DT2 for the (+) class.
Transcribed Image Text:3 Consider the decision trees shown in Figure 1. The decision tree in 1b is a pruned version of the original decision tree 1a. The training and test sets are shown in table 5. For every combination of values for attributes A and B, we have the number of instances in our dataset that have a positive or negative label. 0 3.1 + 0 3.4 B 0 0 0 1 1 0 1 1 ~~ 3.5 2 0 2 1 1 0 + 5 3 22 7 26 A (a) Decision Tree 1 (DT1) 2 1 6 B Training set # of (+) instances #of (-) 1 0 34 3 4 7 32 54 2 5 instances 4 B 1 + Figure 1 Table 5 + 4 0 36352 0 3 + A 1 B Test set # of (+) instances # of (-) instances 3.3 Build the confusion matrices when using DT1 and DT2 to predict for the test set. 1 (b) Decision Tree 2 (DT2) Estimate the generalization error rate of both trees shown in Figure 1 (DT1, DT2) using the optimistic approach and the pessimistic approach. To account for model complexity with the pessimistic approach, use a penalty value of 2 = 2 for each leaf node. Compute the error rate of the DT1 and DT2 on the test set shown in the table 5. 3.2 Which tree would you select? In other words, would you use the original decision tree or would you prune it? Briefly explain how you will decide. 2 1 1 3 15 25 Calculate the test accuracy, precision, recall, and F1-score of DT1 and DT2 for the (+) class.
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