Regression level set estimation via cost-sensitive classification

Regression level set estimation is an important yet understudied learning task. It lies somewhere between regression function estimation and traditional binary classification, and in many cases is a more appropriate setting for questions posed in these more common frameworks. This note explains how estimating the level set of a regression function from training examples can be reduced to cost-sensitive classification. We discuss the theoretical and algorithmic benefits of this learning reduction, demonstrate several desirable properties of the associated risk, and report experimental results for histograms, support vector machines, and nearest neighbor rules on synthetic and real data.