In a typical ROC curve all I do is a line from (0, 0) to (tpr, fpr) and a line from (tpr, fpr) to (1, 1). Now I see ROC curves with more than one points. Can someone explain what these extra points represent?
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$\begingroup$ More than one points is unclear. Perhaps you would upload a picture of what you are asking to clarify, please? Welcome to the site. $\endgroup$ – Carl Sep 29 '16 at 14:31
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That pair TPR, FPR you put in your curve was obtained using a threshold in the continuous output (most likely probabilities).
Other points are obtained by simply changing said threshold.
A clarification: Sampling many points in the ROC curve is the norm, I don't remember ever seeing a ROC with such few samples. You can select different strategies to sample your TPR and FPR, but sampling enough points is essential, otherwise you wouldn't need the ROC at all.
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$\begingroup$ So, is there any typical threshold range or step which is most often used (in case the output is probabilities)? I mean probably a threshold of 0.001 wouldn't make any sense. $\endgroup$ – DimChtz Sep 29 '16 at 14:12
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1$\begingroup$ I just plotted such an ROC curve two days ago. There was one threshold involved, on a predicted probability. I varied that threshold from 0 to 1 in steps of 0.01, classified the sample for each threshold, calculated TPR and FPR for each threshold value, and plotted a 101-point ROC curve. $\endgroup$ – Stephan Kolassa Sep 29 '16 at 14:17
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1$\begingroup$ @DimChtz the full ROC curve can be obtained using every possible threshold, though that is usually unnecessary. Just try to sample uniformly through the curve, or do as Stephan says. $\endgroup$ – Firebug Sep 29 '16 at 14:22
