A year ago, a Black man was arrested for theft. The evidence was crummy face-recognition coupled with a security guard's ID who had not seen the person, only a security tape.

A few months ago, some civil rights organizations filed a lawsuit against the Detroit Police Department for the wrongful arrest.

I want to offer my insight into the issue of arrests based on face recognition.

A game of numbers

Suppose the face recognition system has a one-in-a-million FPR (false positive rate).

Let's also say it has 100% TPR (true positive rate, or "100% recall" - meaning if the guilty person is in the dataset, they will be matched also).

If you search for matches through the 1M faces, and the suspect is among those records, you get on average 1 false positive match, and 1 true positive.

So the people you are arresting only have a 1 in 2 chance of being guilty (though to be completely fair, the police would know something's up if it gets two matches, but here it was apparently just one).

Bigger numbers

If you scale this up ("50 million driver’s license photographs and mug shots contained in a Michigan police database"), you get roughly 50 false positives, and maybe one true positive, if it's in the data. But if the guilty person is not in the dataset, the police only get the false positives.

To be fair, usually you can restrict the suspect pool somehow else. But here, the arrest was based on facial recognition.

Benefit of the doubt

The Detroit Police themselves admit a misidentification rate of 96% - which means the false-positive-to-true-positive ratio is not the 50 we guessed above, but 96/(100-96) = 24.

The tech supplier does not mention the error rate of their product.

However, NIST ran some tests in 2019, which are no longer available on the NIST website, but fortunately they are on archive.org (linked).

(By the way, I find it suspicious that NIST removed this relevant study at a time when this trial begins. In case archive.org deletes it, you can also download it here).

They made roughly 195 billion comparisons between known-differrent people. The False Match Rate (same as our FPR) of algorithms ranges between 1e-6 to 2e-4 (5th to 95th percentiles respectively), or from one-in-a-million to 2-in-10-thousand. This means for each million of comparisons between random people, the algorithms flag about 1 to 200 as false matches.

So, checking a single person against Detroit's 50M database, would yield somewhere between 50 matches to 10k matches. Giving them the benefit of the doubt, and assuming the suspect is indeed in the dataset, that would mean a false-positive-to-true-positive ratio between 50 and 10000.

The value of 24 claimed by the police lies outside this interval, which means it is less than 5% likely that they are telling the truth. But let's assume they do, since technology improves year by year.

More accurate numbers: Race

Fortunately, the NIST report breaks down the false-match-rate by country. On page 42 of the report shows that while the false match rate within E. Europe is at least 1e-6, that for men within W. Africa is at least 7.5e-6, which is 7.5 times worse. For women it's much worse (>10e-6 vs. 1e-6).

This makes it likely that Black people in the US suffer more false positives (if not 7.5 times more), and seeing that "68 out of 70 facial recognition searches were done on Black suspects", this casts further doubt on their claimed 4% success rate.

Conclusion

The abysmal 4% success rate that Detroit Police claim is very optimistic, even putting into question the cases successfully indicted.

Even if it were correct, it would mean a typical search in their database matches 24 innocent people for every legitimate match, and has very limited statistical power, due to the large datasets.

In addition, eyewitness identification uses the same features as the automated one (namely, the face). As such, it is unfit for use as corroboration, as was done in this case.

I will refer to Blackstone's ratio:

It is better that ten guilty persons escape than that one innocent suffer.

The implied performance of one guilty conviction to 24 innocents suffering is far short of Blackstone's ratio (which is itself a minimum; the ideal ratio may be even higher).

Normalizing, we'd get 1/24th of a guilty conviction for every innocent suffering, which is 1/240th of Blackstone's ratio.

As such, a face recognition match could be used as circumstantial evidence at best.