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It's from statistical inference, e.g., when the goal is to find the values of a model's parameters that match the sample. So if the model is y = f(x, params), inference gives you params, and prediction gives you y for a value of x that you haven't seen before.

Also, shouldn't the verb be inferring?

More than that, inference usually refers to acts of decision making or evidence evaluation, like testing hypotheses or interpreting confidence/credible intervals.

Except in AI terminology[1], it seems that inference doesn't mean outputting params. It means outputting y.

Yes, I believe the verb is "inferring".

[1] https://blogs.nvidia.com/blog/2016/08/22/difference-deep-lea...

You're probably right then. I find AI nomenclature to be a bit of a mess.

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