Risk Bounds For Distributional Regression

Carlos Misael Madrid Padilla, OSCAR HERNAN MADRID PADILLA, Sabyasachi Chatterjee

Keywords: Nonparametric distribution estimation, isotonic, trend filtering, dense ReLU networks.

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.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 7401