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:
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:
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?