Risk Bounds For Distributional Regression

2025/05/14 by Carlos Misael Madrid Padilla, Oscar Hernán Madrid Padilla, Padilla, Carlos Misael Madrid +3
Agricultural and Biological Sciences · Mathematics · #Agricultural risk and resilience #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2505.09075

openalex publication_date 2025/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Confidence Interval Construction and Conditional Variance Estimation with Dense ReLU Networks
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• Suboptimality of Constrained Least Squares and Improvements via Non-Linear Predictors