Probability bounds for active learning in the regression problem

TL;DR

This paper develops probabilistic bounds for active learning in regression, proposing batch and online sampling schemes with theoretical guarantees using concentration inequalities.

Contribution

It introduces new probabilistic bounds and sampling strategies for active learning in regression, extending methods from classification to regression problems.

Findings

Derived concentration inequalities for regression sampling schemes

Proposed batch and online active learning algorithms with theoretical guarantees

Bounded deviations of sampling schemes using weighted concentration bounds

Abstract

In this article we consider the problem of 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 following algorithms recently developed for the classification problem. Our main tools are concentration-type inequalities which allow us to bound the supremum of the deviations of the sampling scheme corrected by an appropriate weight function.