That depends completely on what you are using the value for. Recommending five funny articles - GDPR does not apply. Denying an insurance claim - GDPR most certainly applies, and you have to be able to explain what factors went into the decision. You can't have unaccountable oracle boxes.
Note that a perfectly valid answer could be something like "We've analyzed your posts on social media and we've categorized you as having severe anger issues, which is why we're denying this auto collision insurance claim, because you are most likely at fault given situations like this". The GDPR says you have to be able to explain your decision like that. It doesn't forbid you from making these decisions.
> If you took someone's picture and ran it through neural style, would that be illegal because you couldn't tell them exactly why it painted their nose blue
This is not a business decision, don't be ridiculous.
The Chinese Corp API seems like the same thing. "We looked at you and decided you look like someone who wants to go on a Greek vacation."
If you took someone's picture and ran it through neural style, would that be illegal because you couldn't tell them exactly why it painted their nose blue while imitating Leonardo Da Vinci's artistic style? Is Google auto identification of objects in personal images illegal now because they can't explain how a deep neural net works and classified their friend as something non-human by accident? This has actually happened.