Probability bounds for active learning in the regression problem

Abstract

In this article we consider the problem of active learning in the regression setting. That is, choosing an optimal sampling scheme for the regression problem simultaneously with that of model selection. We consider a batch type approach and an on–line approach adapting algorithms developed for the classification problem. Our main tools are concentration–type inequalities which allow us to bound the supreme of the deviations of the sampling scheme corrected by an appropriate weight function.