> no one is trying to do statistical inference using compression
Well, maybe no one sensible? I still think it's quite cool that you can take any general purpose compression algorithm, and abuse it to do e.g. image classification. (Just append the image you want to classify to each of the classes' sets in turn, and see which compresses best!)
And actually I do remember a paper that tried to use ideas from PAQ to do online learning. Gated Linear Networks, out of DeepMind, in 2019:
Well stochastic processes are a much wider category than mere algebraic operations applied on group theory that losseles data compression use.
I'd think that calculus or functional theory or category theory can find more bijections towards statistics or even congruences than mere arithmetics or algebra ever will. Ok, you can explain or derive any mathematics construct using only algebra, and there were efforts to do so, but does it makes sense?
Well, maybe no one sensible? I still think it's quite cool that you can take any general purpose compression algorithm, and abuse it to do e.g. image classification. (Just append the image you want to classify to each of the classes' sets in turn, and see which compresses best!)
And actually I do remember a paper that tried to use ideas from PAQ to do online learning. Gated Linear Networks, out of DeepMind, in 2019:
https://arxiv.org/abs/1910.01526
All compression is related to AI, but especially sample efficient online learning is basically what data compression is all about.