Risk Bounds For Distributional Regression
It provides theoretical guarantees for distributional regression methods, which is important for statisticians and machine learning practitioners, but is incremental as it builds on existing convergence rate frameworks.
This work tackles the problem of establishing risk bounds for nonparametric distributional regression estimators, deriving general upper bounds for the continuous ranked probability score (CRPS) and worst-case mean squared error (MSE), and validating these with experiments on simulated and real data.
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.