We have 10 instances: 5 P and 5 N, given in the following table. Generate a ROC curve and comment on the performance of the classifier. What threshold you will choose? Justify your choice of threshold. Instance Number Class Score 1 P 0.9 0.8 3 P 0.7 4 0.6 0.55 0.5 N 7 0.4 8 N 0.3 9. N 0.2 10 N 0.1 Note: You don't need to write code: vou have to solve this problem using paper and pencil (or

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
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**Educational Content on Generating a ROC Curve**

### Introduction

In the given problem, we have 10 instances: 5 Positive (P) and 5 Negative (N). The table below shows the class and score for each instance. We are tasked to generate a Receiver Operating Characteristic (ROC) curve using this data and to evaluate the classifier's performance. Additionally, we will choose an optimal threshold and justify this choice.

### Data Table

| Instance Number | Class | Score |
|-----------------|-------|-------|
| 1               | P     | 0.9   |
| 2               | P     | 0.8   |
| 3               | P     | 0.7   |
| 4               | P     | 0.6   |
| 5               | N     | 0.55  |
| 6               | N     | 0.5   |
| 7               | P     | 0.4   |
| 8               | N     | 0.3   |
| 9               | N     | 0.2   |
| 10              | N     | 0.1   |

### Instructions

1. **ROC Curve Generation:**
   - The ROC curve is a graphical representation of a classifier's performance. It plots the True Positive Rate (TPR) against the False Positive Rate (FPR) at various threshold settings.
   - To create the ROC curve, calculate the TPR and FPR for different threshold values from the highest score to the lowest.

2. **Threshold Selection:**
   - The threshold determines the score above which an instance is classified as positive.
   - Choose a threshold that balances sensitivity (TPR) and specificity (1 - FPR).
   
3. **Justification of Threshold:**
   - Justify your chosen threshold based on the problem's context. Consider the costs of false positives versus false negatives.

### Note

You do not need to write code; this exercise is intended to be solved using paper and pencil (or equivalent).
Transcribed Image Text:**Educational Content on Generating a ROC Curve** ### Introduction In the given problem, we have 10 instances: 5 Positive (P) and 5 Negative (N). The table below shows the class and score for each instance. We are tasked to generate a Receiver Operating Characteristic (ROC) curve using this data and to evaluate the classifier's performance. Additionally, we will choose an optimal threshold and justify this choice. ### Data Table | Instance Number | Class | Score | |-----------------|-------|-------| | 1 | P | 0.9 | | 2 | P | 0.8 | | 3 | P | 0.7 | | 4 | P | 0.6 | | 5 | N | 0.55 | | 6 | N | 0.5 | | 7 | P | 0.4 | | 8 | N | 0.3 | | 9 | N | 0.2 | | 10 | N | 0.1 | ### Instructions 1. **ROC Curve Generation:** - The ROC curve is a graphical representation of a classifier's performance. It plots the True Positive Rate (TPR) against the False Positive Rate (FPR) at various threshold settings. - To create the ROC curve, calculate the TPR and FPR for different threshold values from the highest score to the lowest. 2. **Threshold Selection:** - The threshold determines the score above which an instance is classified as positive. - Choose a threshold that balances sensitivity (TPR) and specificity (1 - FPR). 3. **Justification of Threshold:** - Justify your chosen threshold based on the problem's context. Consider the costs of false positives versus false negatives. ### Note You do not need to write code; this exercise is intended to be solved using paper and pencil (or equivalent).
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