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Risk Bounds For Distributional Regression

arXiv 2505.09075 ↗First posted 14 May 2025stat.ML cs.LGcited by 0

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Abstract (arXiv)

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.

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References · 17

  1. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 433
  2. 2018Improving Regression Performance with Distributional Lossescited by 67
  3. 2023Engression: Extrapolation through the Lens of Distributional Regressioncited by 51
  4. 2013Adaptive piecewise polynomial estimation via trend filteringcited by 47
  5. 2014Trend Filtering on Graphscited by 45
  6. 2020Distributional Random Forests: Heterogeneity Adjustment and Multivariate Distributional Regressioncited by 37
  7. 2019Isotonic Distributional Regressioncited by 28
  8. 2020Quantile regression with deep ReLU Networks: Estimators and minimax ratescited by 24
  9. 2018Distributional Regression Forests for Probabilistic Precipitation Forecasting in Complex Terraincited by 19
  10. 2022Theoretical analysis of deep neural networks for temporally dependent observationscited by 16
  11. 2019Monotone Least Squares and Isotonic Quantilescited by 7
  12. 2019New Risk Bounds for 2D Total Variation Denoisingcited by 6
5 more
  1. 2020Non-parametric Quantile Regression via the K-NN Fused Lassocited by 4
  2. 2024Dense ReLU Neural Networks for Temporal-spatial Modelcited by 3
  3. 2024Confidence Interval Construction and Conditional Variance Estimation with Dense ReLU Networkscited by 3
  4. 2021Consistent estimation of distribution functions under increasing concave and convex stochastic orderingcited by 1
  5. 2023Spatio-temporal model via Locally Adaptive Regression Splinescited by 1

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