Selective Nonparametric Regression via Testing
This addresses the need for reliable regression models in error-critical applications, offering a novel approach to abstention that accounts for variance uncertainty, though it is incremental in extending selective methods from classification to regression.
The paper tackles the problem of selective prediction in regression, where models can abstain from making predictions in error-critical applications, by developing a nonparametric method that tests the conditional variance at a given point. The result includes proven non-asymptotic risk bounds and experimental validation on simulated and real-world data.
Prediction with the possibility of abstention (or selective prediction) is an important problem for error-critical machine learning applications. While well-studied in the classification setup, selective approaches to regression are much less developed. In this work, we consider the nonparametric heteroskedastic regression problem and develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor. We prove non-asymptotic bounds on the risk of the resulting estimator and show the existence of several different convergence regimes. Theoretical analysis is illustrated with a series of experiments on simulated and real-world data.