Selective Nonparametric Regression via Testing
Fedor Noskov Alexander Fishkov Maxim Panov
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.