Can machine learning can recognize "uncorrelation" between data and label? Sorry for unclear title, but I was not sure how to put this into one sentence.
Recently, I found that there's a site (https://crimetest.ga/) which you can upload one's face picture then the model they trained will classify which type of crime you might possibly commit. They claim that they have trained the classifier model with real criminal faces dataset, however in common sense, there can be no correlation between someone's face and the crime he commits, and it has not been proven scientifically. (I think this site is made by someone who believe ML as a some kind of black box which can, if you put any data X with label Y and train a lot, it can classify any data into label Y.)
Anyway my question is... let's say there are data X and label Y with no such correlation or causal relation between them but we put them together in ML model anyway. Is there any study or paper about if the ML model can certainly recognize the "uncorrelation" between data X and label Y without making wrong assumption or bias? (So for the example above, can one model indicate that there's no correlation between face image and its crime label when the dataset is fed?)
Once again, sorry if my question is unclear or not enough. I had many troubles of describing the question I have in mind into clear English sentences.
p.s.
I have found that training neural network with random label can boost the training (https://arxiv.org/abs/2006.10455) but I don't know if this has something with my question.
Edit:
Just adding few words. If ML cannot recognize "uncorrelation" between data and label, does that mean if I want to know how much the data X and label Y are correleated (or if I desire the data X and label Y to be independent and want to check), it is never a good choice to use ML model for such task?
 A: If there is no such correlation, you can just show that the predictions are not significantly better than the chance level. Using an equivalence test or non-inferiority test, you can show that the correlation is very likely close to 0 or lower than some small value. a
Now, the problem with those phrenology-like studies is not that they cannot correlate with the outcome, but that they would just learn to recognize class, race, socio-economic status, how grumpy or ugly your face is, and then present it as "objective" an innate propensity of the person to commit some crime. However, it is very far from being so.
E.g., you need to work an office job to commit securities fraud, and you are more likely to look a certain way if you work in an office, but that doesn't mean it would be good to now label every pale guy as a potential fraudster and hire truckers and roofers instead.
A: There's a yes and a no to this.
For the yes, that is called overfitting, and it is the enemy of machine learning practitioners.
For the no, if the distribution of features is exactly the same for all levels of the outcome, then nothing will give you an ability to separate the distributions, not even a little bit. You might be able to overfit, just because the samples from those distributions are not identical, but that's all you have done; nothing can separate $N(0,1)$ from $N(0,1)$, for instance.
Back to the yes, however, machine learning might be able to find patterns that are real and useful, perhaps even highly predictive, even if they are unexpected.
