How are True Negative and False Negative converted into True Positive and False Positive in ROC curve?

Question

I found the ROC explanation at this link. It states that the ROC curve is TP vs FP.

After the score has gone below 0.5, all predictions are negative. That makes them either TN or FN. Thus, how does it make sense to continue drawing as the axes are stated as TP and FP? I am really confused.

I think this is a situation where you're probably going to get better explanations for why your understanding is wrong the better you explain what your understanding is. — Acccumulation, Aug 12 '21 at 03:42
I found this very well explained [video](https://www.youtube.com/watch?v=4jRBRDbJemM). I suppose I got it wrong because of the lack of background theory? — CaTx, Aug 12 '21 at 06:12

score 4 · Answer 1 · answered Aug 11 '21 at 17:42

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you vary the threshold which is used to determine positives and negatives, ie at threshold 0.5 we get a point (TP, FP) which we plot, then at threshold 0.45 we get another point (TP, FP) which we plot, etc. These points make the ROC curve

answered Aug 11 '21 at 17:42

bdeonovic

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I dont quite follow your explanation. Say at point `1` (0.9) in that link, which (TP, FP) is acquired from that threshold value? – CaTx Aug 11 '21 at 17:58
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@CaTx The threshold is not graphed in the ROC curve. – Dave Aug 11 '21 at 20:17
Thank you for the clarification! – CaTx Aug 12 '21 at 06:11
some ROCs feature the threshold e.g. as color. E.g. R package ROCR offers this option (and I recommend to use it, this additional information is often highly instructive). – cbeleites unhappy with SX Aug 12 '21 at 10:09

Sycorax · Accepted Answer · 2021-08-11T20:15:11.417

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The ROC curve shows the TPR and FPR as you change the threshold. Your question posits that a classifier only has one TPR statistic and one FPR statistic, and that both of these statistics correspond to a threshold at 0.5. This is a common misconception; there is no reason that the threshold must be 0.5. For each choice of threshold, there is a corresponding TPR and FPR statistic. The purpose of the ROC curve is to show the trade-off for each choice of threshold: as your TPR increases, so does your FPR, and vice-versa.

edited Aug 11 '21 at 20:15

answered Aug 11 '21 at 17:47

Sycorax

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Goodness! You caught the cause of my misunderstanding. – CaTx Aug 11 '21 at 17:56

How are True Negative and False Negative converted into True Positive and False Positive in ROC curve?

2 Answers2