Is Supervised Learning Really That Different from Unsupervised?

ArXi:2505.11006v5 Announce Type: replace-cross We nstrate how supervised learning can be decomposed into a two-stage procedure, where (1) all model parameters are selected in an unsupervised manner, and (2) the outputs y are added to the model, without changing the parameter values. This is achieved by a new model selection criterion that - in contrast to cross-validation - can be used also without access to y. For linear ridge regression, we bound the asymptotic out-of-sample risk of our method in terms of the optimal asymptotic risk.