$H$-Consistency Guarantees for Regression

arXiv:2403.19480v1 Announce Type: new
Abstract: We present a detailed study of $H$-consistency bounds for regression. We first present new theorems that generalize the tools previously given to establish $H$-consistency bounds. This generalization proves essential for analyzing $H$-consistency bounds specific to regression. Next, we prove a series of novel $H$-consistency bounds for surrogate loss functions of the squared loss, under the assumption of a symmetric distribution and a bounded hypothesis set. This includes positive results for the Huber loss, all $\ell_p$ …

abstract arxiv cs.lg functions loss next novel prove regression series stat.ml study tools type