# Selective Nonparametric Regression via Testing

arXiv: https://arxiv.org/abs/2309.16412 · HTML: https://mlsanity.com/paper/2309.16412/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 25 references that are in the map.
- First posted on arXiv 28 Sep 2023.

## Builds on (most cited first, 5 of 5)

- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [Selective Regression Under Fairness Criteria](https://mlsanity.com/paper/2110.15403/) (2021)
- [Regression with reject option and application to kNN](https://mlsanity.com/paper/2006.16597/) (2020)
- [Exponential Savings in Agnostic Active Learning through Abstention](https://mlsanity.com/paper/2102.00451/) (2021)
- [Fast Rates for Online Prediction with Abstention](https://mlsanity.com/paper/2001.10623/) (2020)

## Abstract (arXiv)

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.