You are evaluating a binary classifier. There are 50 positive outcomes in the test data, and 100 observations. Using a 50% threshold, the classifier predicts 40 positive outcomes, of which 10 are incorrect.Increasing the threshold to 60% results in 5 additional positive predictions, all of which are correct. Which of the following statements about this new model (compared with the original model that had a 50% threshold) is TRUE?1 pointThe F1 score of the classifier would decrease.The area under the ROC curve would decrease.The F1 score of the classifier would remain the same.The area under the ROC curve would remain the same.
Question
You are evaluating a binary classifier. There are 50 positive outcomes in the test data, and 100 observations. Using a 50% threshold, the classifier predicts 40 positive outcomes, of which 10 are incorrect.Increasing the threshold to 60% results in 5 additional positive predictions, all of which are correct. Which of the following statements about this new model (compared with the original model that had a 50% threshold) is TRUE?1 pointThe F1 score of the classifier would decrease.The area under the ROC curve would decrease.The F1 score of the classifier would remain the same.The area under the ROC curve would remain the same.
Solution
To answer this question, we first need to understand the concepts of F1 score and ROC curve.
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F1 Score: It is the harmonic mean of precision and recall. Precision is the number of true positive results divided by the number of all positive results. Recall is the number of true positive results divided by the number of positive results that should have been returned.
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ROC Curve: It is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied.
Now, let's calculate the F1 score and ROC curve for both the models.
For the original model (50% threshold):
- True Positives (TP): 40 - 10 = 30
- False Positives (FP): 10
- False Negatives (FN): 50 - 30 = 20
- Precision: TP / (TP + FP) = 30 / (30 + 10) = 0.75
- Recall: TP / (TP + FN) = 30 / (30 + 20) = 0.6
- F1 Score: 2 * (Precision * Recall) / (Precision + Recall) = 2 * (0.75 * 0.6) / (0.75 + 0.6) = 0.6667
For the new model (60% threshold):
- True Positives (TP): 40 - 10 + 5 = 35
- False Positives (FP): 10
- False Negatives (FN): 50 - 35 = 15
- Precision: TP / (TP + FP) = 35 / (35 + 10) = 0.7778
- Recall: TP / (TP + FN) = 35 / (35 + 15) = 0.7
- F1 Score: 2 * (Precision * Recall) / (Precision + Recall) = 2 * (0.7778 * 0.7) / (0.7778 + 0.7) = 0.7368
As we can see, the F1 score of the classifier has increased from 0.6667 to 0.7368. Therefore, the statement "The F1 score of the classifier would decrease" is FALSE.
The ROC curve is a plot of the true positive rate (TPR) versus the false positive rate (FPR) at various threshold settings. Increasing the threshold to 60% results in an increase in both TPR and FPR. Therefore, the area under the ROC curve would not necessarily decrease or remain the same. It depends on the specific distribution of the data. Therefore, we cannot definitively say whether the statements "The area under the ROC curve would decrease" or "The area under the ROC curve would remain the same" are true or false without more information.
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