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.The threshold is now increased further, to 70%. Which of the following statements is TRUE?1 pointThe Recall of the classifier would Increase.The Precision of the classifier would decrease.The Recall of the classifier would increase or remain the same.The Precision of the classifier would increase or 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.The threshold is now increased further, to 70%. Which of the following statements is TRUE?1 pointThe Recall of the classifier would Increase.The Precision of the classifier would decrease.The Recall of the classifier would increase or remain the same.The Precision of the classifier would increase or remain the same.
Solution
The Precision of the classifier would increase or remain the same.
Here's why:
First, let's define the terms:
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Precision is the proportion of true positive predictions (correct positive predictions) out of all positive predictions. It's calculated as True Positives / (True Positives + False Positives).
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Recall (or sensitivity) is the proportion of true positive predictions out of all actual positive outcomes. It's calculated as True Positives / (True Positives + False Negatives).
In the initial scenario, we have 40 predicted positive outcomes, of which 10 are incorrect. This means we have 30 True Positives and 10 False Positives. So, the initial precision is 30 / (30 + 10) = 0.75.
When we increase the threshold to 70%, the classifier becomes more conservative about predicting a positive outcome. This means it's less likely to predict a positive outcome unless it's very confident. As a result, the number of False Positives (incorrect positive predictions) is likely to decrease.
Since False Positives decrease, the denominator in the precision calculation (True Positives + False Positives) decreases. As long as the number of True Positives doesn't decrease faster than the False Positives, the precision would increase or remain the same.
On the other hand, recall might decrease because by raising the threshold, the model might miss some actual positive cases (increasing False Negatives), but this isn't a given option in your question.
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