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A quick overview of definitions before I get into the question:

  • True Positive (TP): An actual positive that the model classified as positive

  • False Positive (FP): An actual negative that the model classified as positive

  • False Negative (FN): An actual positive that the model classified as negative

  • Recall (True Positive Rate, TPR): $\frac{TP}{TP + FN}$

  • Precision: $\frac{TP}{TP + FP}$

  • Logistic Threshold: A probability above which a sample is classified as positive and below which is classified as negative. It is the grey line in the figure: enter image description here

  • Confusion Matrix: Summary of classification results

  • Steps to generating Precision-Recall curve: 1.) Choose a threshold. 2.) Generate confusion matrix. 3.) Calculate the TPR and Precision from confusion matrix and plot the point

  • Example of Precision-Recall curve:

enter image description here

We can see from this example that the precision is 1 when the recall is 0. I find this confusing...


My question:

Let's say we choose a threshold of 1. Thus, all the samples will be classified as negatives. Thus there will be no true positives, no false positives, and likely a bunch of false negatives.

The calculated recall (TPR) would be: $\frac{0}{0 + FN} = 0$

The calculated precision would be: $\frac{0}{0 + 0} = \frac{0}{0}$

So how come the precision-recall curves I see have precision = 1 when recall (TPR) = 0?

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You can't divide by zero, so precision is undefined. It's a pathological case, so it doesn't return meaningful results.

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  • $\begingroup$ The logistic regression model is a probability model. What you are doing is inappropriate for this model. $\endgroup$ Apr 18 at 11:15

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