Comment by m12k
20 hours ago
The intuition I've built is that you can't talk about a false positive rate being high or low on its own - it's always relative to the actual occurrence rate of positives in the tested population. E.g. if there's a 1 in 10000 risk of a false positive, but real positives also are only 1 out of 10000 tested cases, then a positive case will have a 50/50 chance of being a false positive (because for every 10000 tests, you'll have on average one false positive and one real positive). So a false positive rate can only be said to be low if it's significantly lower than the real occurrence rate of positives.
The mentioned accuracy in the comment you are replying to already encapsulates the relation of true positives to false positives.
No I don't believe it does. I interpret 99.9% accurate to mean 1 in 1000 false positives. If 0.1% of your population are terrorists that means each alert has a 50% chance of being correct. That's nowhere near good enough to fully automate things but it is quite reasonable assuming this is merely information provided to a human agent.
Whereas if only 0.001% of your population are terrorists then 99 out of 100 alerts are false positives at which point the system is well on its way to being useless.
There is an important difference between scenarios where we care about the relative versus absolute frequency of errors.
You're right it doesn't. At least not completely. I was thinking about precision (i.e.: if the test is positive, what are the odds that its prediction is true). It turns out, that accuracy is not defined as "true positive / (true pos. + true neg.)", but "correct predictions / all predictions". The whole point of OP's statement: "It's kind o remarkable how even a 99.9% accurate heuristic is insufficient at scale.", which you actually support with your example.
> There is an important difference between scenarios where we care about the relative versus absolute frequency of errors.
The context is chat control without probable cause over the whole population of Europe with a low prevalence. My point, and presumably that of OP, is that even a small relative frequency of errors will yield an unsustainably high absolute frequncy of errors.
> This is merely information provided to a human agent.
It will be in theory. In practice the human agent will just forward the decision. A human agent is not sufficient; you need to test only with probable cause for the kind of scenario we're talking about. The exact opposite of "Chat Control 1.0 and 2.0".
P.S.: The comment I originally replied to choose a very convoluted way of saying that the false discovery rate of the test matters for a proper evaluation. Both you and they explain this by throwing numbers without context in combination with slightly inaccurate definitions. I got the definitions mixed up differently, which led to this follow-up.
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It really doesn’t, and it is easy to demonstrate by using an extreme example.
Suppose I invent a device that can detect whether there is a giant invisible dragon living in your house, and it has an accuracy of 99.999%
Now, I use it in your house and it tells me there is an invisible dragon… so what are the chances that there is a dragon in your house?
Based on your statement, it would be 99.999% likely that there is an invisible dragon in your house. However, we actually know that there is a 0% chance there is an invisible dragon, so even with the positive test result we still know there is a 0% chance a dragon is there.
False result rate is a property of the test. They're describing predictive value, derived from that rate and population statistics.
https://en.wikipedia.org/wiki/Positive_and_negative_predicti...