Research map / Learning theory and algorithms / Kernels and regression theory
Distributional regression: CRPS-error bounds for model fitting, model selection and convex aggregation
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Gives non-asymptotic CRPS-error bounds for CRPS empirical risk minimization of parametric distributional regression models, and for validation-based model selection and convex aggregation, under sub-Gaussian and moment assumptions, illustrated with KNN and DRF on QSAR and Airfoil data.
Problem
Lack of statistical learning guarantees for distributional regression fitted by CRPS minimization, covering model fitting, model selection and convex aggregation.
Approach
Derives concentration bounds for the CRPS excess risk of ERM (via a covering argument using the 2-Lipschitz property of CRPS in Wasserstein-1), and regret bounds for validation-based model selection and convex aggregation, under sub-Gaussian assumptions and extended to finite p-th moment assumptions.
Key results
- On QSAR, convex aggregation achieved mean test CRPS 0.612 vs 0.624 for DRF, 0.632 for model selection, and 0.643 for KNN (100 random splits).
- Validation-selected hyperparameters on QSAR were k=8 (KNN, validation CRPS 0.696) and mtry=4 (DRF, validation CRPS 0.678).
- Theory: ERM excess-risk oracle inequality of order sqrt(log(n^K)/n) under sub-Gaussianity, with L^p rate n^{-p/(2(p+K))} under moment assumptions.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DRF instead of KNN | KNN and DRF · QSAR aquatic toxicity test | CRPS: 0.643 -> 0.624 | Helped |
| Select between KNN and DRF using validation CRPS | KNN and DRF · QSAR aquatic toxicity test | CRPS: 0.624 -> 0.632 | Hurt |
| Optimize convex aggregation weights using validation CRPS | KNN and DRF · QSAR aquatic toxicity test | CRPS: 0.624 -> 0.612 | Helped |
Limitations
- Results rely on sub-Gaussian or moment assumptions on Y and on the absolute moment of predictive distributions, plus compact parameter spaces and Lipschitz models.
- Experiments are small-scale with only two datasets and only KNN and DRF models; the paper notes minimax rates and empirical process extensions are future work.
Experimental setup
Datasets: QSAR aquatic toxicity Airfoil Self-Noise
Benchmarks: QSAR aquatic toxicity Airfoil Self-Noise
Metrics: CRPS mean test CRPS standard error
Baselines: KNN DRF
Builds on: EMOS Distributional Regression Networks Distributional Random Forest Quantile regression forest
Closest papers by meaning
- Risk Bounds For Distributional Regression (NeurIPS 2025 · similarity 0.89)
- Credal Learning Theory (NeurIPS 2024 · similarity 0.83)
- Bayesian Additive Distribution Regression (NeurIPS 2026 · similarity 0.83)
- Bayesian Nonparametrics Meets Data-Driven Distributionally Robust Optimization (NeurIPS 2024 · similarity 0.83)
- Optimal Aggregation of Prediction Intervals under Unsupervised Domain Shift (NeurIPS 2024 · similarity 0.82)
- Credal Wrapper of Model Averaging for Uncertainty Estimation in Classification (ICLR 2025 · similarity 0.82)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.