If I am correct, “unsupervised classification” is same as clustering. Then is there “unsupervised regression”? Thanks!
I’ve never encountered this term before. I am unsure whether it would spread light or darkness within either realm of statistics: those being machine learning (where supervised and unsupervised distinctions are central to problem solving) and inferential statistics (where regression, confirmatory analysis, and NHSTs are most often employed).
Where those two philosophies overlap, the majority of regression and associated terminology is thrown around in a strictly supervised setting. However, I think many existing concepts in unsupervised learning are closely related to regression based approaches, especially when you naively iterate over each class or feature as an outcome and pool the results. An example of this is the PCA and bivariate correlation analysis. By applying best subset regression iteratively over a number of variables, you can do a very complex sort of network estimation, as is assumed in structural equation modeling (strictly in the EFA sense). This, to me, seems like an unsupervised learning problem with regression.
However, regression parameter estimates are not reflexive. For simple linear regression, regressing Y upon X will give you different results, different inference, and different estimates (not even inverse necessarily), than X upon Y. In my mind, this lack of commutativity makes most naive regression applications ineligible for unsupervised learning problems.