Assuming that's true, no wonder the computer did better. I'd bet it would do far worse dealing with a more representative sample.
Still, even though it's not a perfect study, it's still impressive it can do as well as it did.
Very good explanation (though the op's one are too)
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 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
P(being depressed | trivial detector said so) = d * 1.0 / 1.0 = d
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%?
The denominator should be the probability of the classifier being positive: P(True Positive)+P(False Positive)
Since you assumed that P(False Positive) = P(False Negative) = (1-P(True Positive))/2 = (1-P(True Negative))/2
In the algorithm case the denominator is 0.8x0.04+0.1x0.96=0.128
In the human case the denominator is 0.6x0.04+0.2x0.96=0.216
In summary, if a human thinks someone is homosexual, the probability increases to 11.1%. If the algorithm makes that call the probability increases to 25%.
This assumption is usually wrong when trying to detect rare events (such as CC fraud or straight/gay people).
In my own experience, if you train on a prepared 50/50 dataset to some kind of reasonable accuracy, on actual data where classes are more like 96/4 you get a LOT of false positives, thus making the whole thing not very useful
0. https://en.wikipedia.org/wiki/LGBT_demographics_of_the_Unite...
Where in the article does it say that? I can see
> Studies from several nations, including the U.S., conducted at varying time periods, have produced a statistical range of 1.2[4] to 6.8[6] percent of the adult population identifying as LGBT.
but there's no indication of how likely any part of that range is.
Just read the whole article. The references cited are also worth reading if you are actually interested in learning about this topic.
Why are you using the accuracy as a conditional likelihood?
It seems to have infected a lot of the sites I visit, and is always liked or voted to the top.
I guess people just love feeling superior.
According to Gallup Polling, around 4% of the American population is homosexual. So, let's be generous and say that their classifier has a 80% accuracy given balanced inputs while humans have 60%.
Let's sample 100 people of the dataset, 50 of which are homosexual (and the rest heterosexual). If the classifier has 80% accuracy (let's assume false_positive_rate = false_negative_balance since I didn't find information about that), it means that 80 people were correctly classified, 10 heterosexuals were misclassified as homosexuals and 10 homosexuals as heterosexuals.
According to the Bayes theorem, "Given a random person, probability of being homosexual assuming that the classifier said so" = "Probability of being homosexual of a random person (the so-called prior)" <times> "Probability of classifier saying it's homosexual, assuming it's indeed homosexual <divided by> "Given a random person, probability of saying it's homosexual".
Substituting, we get: P = 0.04 * 0.8 / 0.5 = 0.064
If instead of the classifier we use human "feeling", we get: P=0.04 * 0.6 / 0.5 = 0.048
In summary, 4% of the people are homosexual. If a human thinks someone is homosexual, the probability "increases" to 4.8%. If on the contrary their algorithm believes it's homosexual, the probability of actually being homosexual increases to 6.4%.
Not very groundbreaking...