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
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
Section: Chapter Questions
Problem 1PE
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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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