# How can I interprete ROC-curves? (example inside)

I will be writing an exam in machine learning and am preparing for it. During my studies I encountered ROC-curves but I can't wrap my head around what they actually tell you.

I have the following ROC-curves:

First of all the x-Axis is false-alarms, the y-Axis is the hits.

Now the questions from old exams was to say which of these curves would be better for

• image recognition for smartphones
• testing somebody for the ebola-virus/bomb-detector at an airport

Intuitively, the first one should have many hits, the second one can have false alarms, since I want to be sure that if there is a bomb, I recognize it. If there is no bomb I still tolerate false alarms, since better be safe than sorry, right?

But which of the both curves A and B belong to which statement? What do the curves mean?

Traditionally, with screening tests for a disease one seeks an ROC curve that bends up near the upper-left corner, such as "A." Also, a curve that dips below the 45-degree line (separating upper-left from lower right) is not favored.

False alarms for diseases and bomb threats are expensive (extra expensive 'gold standard' testing required, inconvenience discourages participation). However, ebola is hardly a typical disease.

If there are too many false alarms at an airport the method falls out of use because of the excessive disruption. "Better safe than sorry" is hard to argue against until you face the consequences of it.

Depending on user's personality and needs, "B" might be OK for an iPhone. Maybe lots of false alarms are tolerated because of the advantage of correct IDs which may be reminders ("Oh yeah, Sven Rasmusson, the prospective Swedish client from the happy hour last month.") , vs. false alarms that could be instantly dismissed as "Somebody I never heard of."

IMHO you are being asked a mainly-philosophical question rather than a mathematical one, which may not be totally appropriate for such an exam. Might be OK if there is a suitable philosophical discussion in the course that gives clues to the author's opinion. For an exam question, the author's opinion is the only thing that matters.

Anyhow, it seems your main question was how to understand the curve. Maybe this answer will help with that. Maybe other Answers will be more helpful with the philosophical issues--towards a 'correct' answer to the exam question.

• Thank you very much. Your question was more than useful. I remember having a discussion about it in the lecture. The curves were a little different but I don't remember which one should be which. I would argue curve A is the image recognition (because in the lecture there was a "typical" curve which was classified as image recognition and kinda looked like A) which would lead me to question why B is the detector. Seems like my prof doesn't really see the negative outcomes of many false alarms, it is also possible that he just wanted to show us how it looks like in general(?) Commented Jul 15, 2019 at 10:55
• A screening test is intended to be helpful. With ebola: How many false-positive subjects is it ethical to confine in a ward with others who have tested positive without confirmation? When word gets around that those with positive tests are confined, how many people will willingly submit to testing? Will predictive power of pos test P(Disease | Pos Test) be made public? "Better safe than sorry" for whom? // Rhetorical questions. Commented Jul 15, 2019 at 16:08