2You are given the count matrix in the table 4 for the attribute "Previous GPA". The class label is whethera student will pass (C1) or fail (CO) a class. We want to use the attribute "Previous GPA" asour splittingattribute in an inner node of a decision tree with a binary test condition. Which is the best way to partitionthe attribute values into two groups? Form the count matrices for the different partitions and compute theclassification error. Explain your reasoning while considering the metric of classification error to evaluatethe different partitions.03.1+03Consider the decision trees shown in Figure 1. The decision tree in 1b is a pruned version of the originaldecision tree 1a. The training and test sets are shown in table 5. For every combination of values forattributes A and B, we have the number of instances in our dataset that have a positive or negative label.B2210101010+5A3227126Bad1pass (C1)fail (CO) 4B(a) Decision Tree 1 (DT1)1342Table 473254Training setAB # of (+) instances #of (-) instances0011Pre ious GPAFair Good Very goodB641+Figure 1Table 5933+3043635200+A1B2(b) Decision Tree 2 (DT2)Test set# of (+) instances # of (-) instances1131525Estimate the generalization error rate of both trees shown in Figure 1 (DT1, DT2) using the optimisticapproach and the pessimistic approach. To account for model complexity with the pessimistic approach,use a penalty value of 2 = 2 for each leaf node.

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2 You are given the count matrix in the table 4 for the attribute "Previous GPA". The class label is whether a student will pass (C1) or fail (CO) a class. We want to use the attribute "Previous GPA" asour splitting attribute in an inner node of a decision tree with a binary test condition. Which is the best way to partition the attribute values into two groups? Form the count matrices for the different partitions and compute the classification error. Explain your reasoning while considering the metric of classification error to evaluate the different partitions. pass (C1) fail (CO) Bad 1 4 Table 4 Pre ious GPA Fair 6 4 Good Very good 9 3 3 0

2 You are given the count matrix in the table 4 for the attribute "Previous GPA". The class label is whether a student will pass (C1) or fail (CO) a class. We want to use the attribute "Previous GPA" asour splitting attribute in an inner node of a decision tree with a binary test condition. Which is the best way to partition the attribute values into two groups? Form the count matrices for the different partitions and compute the classification error. Explain your reasoning while considering the metric of classification error to evaluate the different partitions. pass (C1) fail (CO) Bad 1 4 Table 4 Pre ious GPA Fair 6 4 Good Very good 9 3 3 0

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Use of XOR function

XOR function or exclusive OR function was introduced in Excel 2013. This function is available under excel logical functions. For the given statement, the XOR function will return true only when either of the statements is true. It returns false when both the statements are true or when both the statements are false.

Question

2
You are given the count matrix in the table 4 for the attribute "Previous GPA". The class label is whether
a student will pass (C1) or fail (CO) a class. We want to use the attribute "Previous GPA" asour splitting
attribute in an inner node of a decision tree with a binary test condition. Which is the best way to partition
the attribute values into two groups? Form the count matrices for the different partitions and compute the
classification error. Explain your reasoning while considering the metric of classification error to evaluate
the different partitions.
0
3.1
+
0
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.
B
2
2
1
0
1
0
1
0
1
0
+
5
A
3
22
7
1
2
6
Bad
1
pass (C1)
fail (CO) 4
B
(a) Decision Tree 1 (DT1)
1
3
4
2
Table 4
7
32
5
4
Training set
A
B # of (+) instances #of (-) instances
0
0
1
1
Pre ious GPA
Fair Good Very good
B
6
4
1
+
Figure 1
Table 5
9
3
3
+
3
0
4
3
6
3
5
2
0
0
+
A
1
B
2
(b) Decision Tree 2 (DT2)
Test set
# of (+) instances # of (-) instances
1
1
3
15
2
5
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.

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