Explain the mechanism, please. It seems wildly implausible to me that someone's facial features change (let alone in a predictable way) once they've committed a crime.
However, I can easily imagine this "working" by keying off things like age/race/gender, which will get you a value that's "better than chance" but isn't, really. Ditto for differences in the photos; nobody smiles in a mugshot, after all.
Your facial features don't change after you do a crime (except maybe for some new prison tats). They don't need to change to keep criminal classification from head shots.
Age, race, gender, income, attractiveness, testosterone levels, gang membership, attention to grooming, addiction, etc. are all predictive of crime, and part of the face picture you use.
Sure, there is some bias in how you label a criminal (convicted of a crime, self-report, etc.), but prediction is possible (without exploiting leakage like smiles or lighting).
Just from a hot-or-not rating I can make an educated guess of your conviction rate and sentencing length.
You made my point for me as you slipped from "criminal classification" to "predictive of crime". They are /NOT/ equivalent.
I have absolutely no doubt that features like age, race, and gender can be associated, at a group level, with crime. I'm also sure all of these can be extracted from face images. At the same time, these data are obviously not enough to make subject-level predictions. At best, this is a prior and even that is contaminated with all kinds of systematic biases.
Suppose you're hiring. You are certainly allowed—and sometimes required—to not hire criminals. If you systematically avoid hiring people with features "predictive of crime", an employment lawyer is going to slap you into tomorrow with a totally justified, slam-dunk of an employment discrimination case.
However, I can easily imagine this "working" by keying off things like age/race/gender, which will get you a value that's "better than chance" but isn't, really. Ditto for differences in the photos; nobody smiles in a mugshot, after all.
(And yes, I know about the paper purporting to show this [https://arxiv.org/pdf/1611.04135.pdf] I just think it's ridiculous)