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So now we know that the threshold is about 30 photos. And we know this: >"The threshold is set to provide an extremely high level of accuracy and ensures less

So now we know that the threshold is about 30 photos. And we know this: >"The threshold is set to provide an extremely high level of accuracy and ensures less than a one in one trillion chance per year of incorrectly flagging a given account." Does that mean they expect about one in every 2.5 people per year to have at least a single false positive image match? (2.512^30 = a trillion)

notJim 5y ago
You need 30 matches before they do anything, so a single false positive wouldn't cause anything to happen.
andrewmcwatters 5y ago
I don't understand why they mention this probability, because it's useless to me without other information. "How fast were you going?" "30." "30 what?" "...Speed."
tehnub 5y ago
To get the probability of a single false positive match, you need to look at the CDF of the binomial distribution [0]. Let X be the number of matches in your iCloud library. Assuming each photo's probability of a match is independent of other photos in the library (shaky assumption), then X ~ Binomial(n, p), where n is the number of photos in the library, and p is the probability of match. The free plan, which gives 5GB, will store up to 2500 photos taken on a 5 megapixel camera. Assuming that's the most common library size, n = 2500. So we need to solve for p given P(X ≥ 30) = 1/trillion and X ~ Binomial(2500, p). Notice P(X ≥ 30) = 1 - P(X ≤ 29), and we can use the CDF formula to get 1 - P(X ≤ 29) = 1 - sum_{k=0}^{29} of (2500 choose k) (1 - p)^k p^(2500 - k). Set that equal to 1/trillion and solve for p. I don't have an easy way to compute that, unfortunately. [0]: https://en.wikipedia.org/wiki/Binomial_distribution#Cumulative_distribution_function https://en.wikipedia.org/wiki/Binomial_distribution#Cumulati...