Ok, maybe this is a really dumb question, but has anyone ever considered extending some of the statistical learning methods to live in some space other that $\mathbb R^n$? My guess is that you're just shuffling parameters around, but I wonder if there's any intuition to be gained. This question came up as I was working through some course notes on neural nets, and realized that computer scientists may be even more cavalier with tensor indices than physicists :)
Machine Learning on Curved Background
machine learning