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I think there are various categories for types of AI/ML right? Like, neural nets, expert systems, Bayesian systems? Idk. I should really learn more about this topic.
"AI" is a vague and all encompassing term used to describe computers making decisions.
Machine learning, yeah, is what you're describing. If you're interested in learning more, look into writing your own neural nets from scratch using any number of programming languages. They're actually a fairly simple concept to both understand and apply in practice, but they can become fairly complex at scale.
Do you happen to have a good guide for writing your own machine learning algo? Ideally not relying on Python libs?
The best thing I can recommend is to just pick your most comfortable language and find guides specific to that.
It's functionally the same regardless of language, however it's much easier to learn as you build it.