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What is the field of machine learning studying specifically prediction/data correlation?

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Suppose I have 2 datasets and I want to know if there is any correlation between them. For example, a set of pictures and a boolean containsCat. I want a system that, given a few samples, finds a generalization. Simple as that.

I know this is an artificial intelligence problem, but the field is so huge I'm not sure what are the right keywords to look at it. I know neural networks are a tool, but it is just one tool. If I google for it I will probably be missing a lot.

So what exactly is the name of that problem, and what is a good starting point for learning the state of art takes on it? What are the relevant keywords?

submitted by SrPeixinho
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