(1) College of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P. R. China;(2) School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, P. R. China
Abstract:
The learning approach of empirical risk minimization (ERM) is taken for the regression problem in the least square framework. A standard assumption for the error analysis in the literature is the uniform boundedness of the output sampling process. In this paper we abandon this boundedness assumption and conduct error analysis for the ERM learning algorithm with unbounded sampling processes satisfying an increment condition for the moments of the output. The key novelty of our analysis is a covering number argument for estimating the sample error.