Risk Bounds For Distributional Regression
Carlos Misael Madrid Padilla, OSCAR HERNAN MADRID PADILLA, Sabyasachi Chatterjee
Abstract
This work examines risk bounds for nonparametric distributional regression estimators. For convex-constrained distributional regression, general upper bounds are established for the continuous ranked probability score (CRPS) and the worst-case mean squared error (MSE) across the domain. These theoretical results are applied to isotonic and trend filtering distributional regression, yielding convergence rates consistent with those for mean estimation. Furthermore, a general upper bound is derived for distributional regression under non-convex constraints, with a specific application to neural network-based estimators. Comprehensive experiments on both simulated and real data validate the theoretical contributions, demonstrating their practical effectiveness.
BibTeX
@inproceedings{
padilla2025risk,
title={Risk Bounds For Distributional Regression},
author={Carlos Misael Madrid Padilla and OSCAR HERNAN MADRID PADILLA and Sabyasachi Chatterjee},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=Wav9TP5SOR}
}