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Comment by dangom | Hacker News Reader

I don't know if I can follow. You say that if their classifier had 100% accuracy, then the probability of being homosexual would increase to 8%? That doesn't make much sense.

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Look here [1]

Very good explanation (though the op's one are too)

[1]: https://en.wikipedia.org/wiki/False_positive_paradox

But why does "Given a random person, probability of saying it's homosexual" equal 0.5? I'd say that should be 0.04.

I guess because the algorithm has been trained on 50% straight 50% gay and the 80% figure is actually for telling appart a pair of straight and gay persons, it will say gay half the time.. But this is confusing you are right. The explanation using false positive is clearer.

If there is 1000 persons, 40 gay, and the algorithm is 80% accurate, it will say: 960 * 20%= 192 straight people are gay and 40 * 80% = 32 gay person are gay. Not very impressive and shows a very stong gay bias if I can say so

This is the part of his explanation I find confusing too, though I do agree with his general argument: the results aren't really useful when they haven't been tested on a dataset representative of the real distribution.

From what I can gather he's basically saying that the "probability of a random face being classified as homosexual" is 0.5. This isn't REALLY true (would have to run the classifier on all possible faces to find this), but that is in fact the "environment" the classifier has been trained within.

If the test set of images really were 50/50 and the human judges weren't told that, then they were effectively given inaccurate priors, which would obviously reduce their accuracy.

There is also https://en.wikipedia.org/wiki/Base_rate_fallacy, which describes the common mistakes interpreting these kinds of data.

I found that confusing, too. I guess that's the best you can expect if you train your model in such an unrealistically balanced dataset. Put it differently. If I had 100% accuracy at detecting depression in a dataset of depressed people, how well will run this "detector" at detecting depression in the real world? Well, being 'd' the incidence of depression:

P(being depressed | trivial detector said so) = d * 1.0 / 1.0 = d

It doesn't make sense, but that's exactly right. If their training sample had been only 4% gay and achieved 100% accuracy, then the true positive rate would be expected to be 1, because the denominator changes to 0.04.

It does raise the question of how Bayes' rule applies if your sample is underrepresented, though... say their training set was only 2% gay. Could they achieve a true positive rate of 200%?

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