mlsanityData to 7 Oct 2026

CRPS Learning

arXiv 2102.00968 ↗First posted 1 Feb 2021stat.ML cs.LG econ.EMcited by 21

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Abstract (arXiv)

Combination and aggregation techniques can significantly improve forecast accuracy. This also holds for probabilistic forecasting methods where predictive distributions are combined. There are several time-varying and adaptive weighting schemes such as Bayesian model averaging (BMA). However, the quality of different forecasts may vary not only over time but also within the distribution. For example, some distribution forecasts may be more accurate in the center of the distributions, while others are better at predicting the tails. Therefore, we introduce a new weighting method that considers the differences in performance over time and within the distribution. We discuss pointwise combination algorithms based on aggregation across quantiles that optimize with respect to the continuous ranked probability score (CRPS). After analyzing the theoretical properties of pointwise CRPS learning, we discuss B- and P-Spline-based estimation techniques for batch and online learning, based on quantile regression and prediction with expert advice. We prove that the proposed fully adaptive Bernstein online aggregation (BOA) method for pointwise CRPS online learning has optimal convergence properties. They are confirmed in simulations and a probabilistic forecasting study for European emission allowance (EUA) prices.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 12 of its 83 references that are in the map. First posted on arXiv 1 Feb 2021.

Builds on

12 of 83 references.

References · 12

  1. 2018Online Learning: A Comprehensive Surveycited by 203
  2. 2014A Second-order Bound with Excess Lossescited by 91
  3. 2015Second-order Quantile Methods for Experts and Combinatorial Gamescited by 47
  4. 2019Lipschitz Adaptivity with Multiple Learning Rates in Online Learningcited by 36
  5. 2014Optimal learning with Bernstein Online Aggregationcited by 35
  6. 2015Bayesian model averaging: A systematic review and conceptual classificationcited by 29
  7. 2020Online Hierarchical Forecasting for Power Consumption Datacited by 9
  8. 2018Efficient online algorithms for fast-rate regret bounds under sparsitycited by 8
  9. 2019Mixability of Integral Losses: a Key to Efficient Online Aggregation of Functional and Probabilistic Forecastscited by 7
  10. 2020Kalman Recursions Aggregated Onlinecited by 3
  11. 2017A Multi-model Combination Approach for Probabilistic Wind Power Forecastingcited by 2
  12. 2020Sequential Aggregation of Probabilistic Forecasts -- Applicaton to Wind Speed Ensemble Forecastscited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 6; 2023: 4; 2024: 5; 2025: 1; 2026: 5.

21 papers.

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  1. 2022Adaptive Conformal Predictions for Time Seriescited by 155
  2. 2022Forecast combinations: an over 50-year reviewcited by 34
  3. 2022A review of predictive uncertainty estimation with machine learningcited by 29
  4. 2022Distributional neural networks for electricity price forecastingcited by 24
  5. 2022Probabilistic forecasting of German electricity imbalance pricescited by 10
  6. 2023Adaptive Probabilistic Forecasting of Electricity (Net-)Loadcited by 8
  7. 2024Postprocessing of point predictions for probabilistic forecasting of day-ahead electricity prices: The benefits of using isotonic distributional regressioncited by 7
  8. 2022Deep interpretable ensemblescited by 5
  9. 2023Multivariate Probabilistic CRPS Learning with an Application to Day-Ahead Electricity Pricescited by 4
  10. 2023Inductive biases in deep learning models for weather predictioncited by 3
  11. 2023Combining predictive distributions of electricity prices: Does minimizing the CRPS lead to optimal decisions in day-ahead bidding?cited by 3
  12. 2024Experimental Comparison of Ensemble Methods and Time-to-Event Analysis Models Through Integrated Brier Score and Concordance Indexcited by 2
9 more
  1. 2024Improving probabilistic forecasts of extreme wind speeds by training statistical post-processing models with weighted scoring rulescited by 2
  2. 2024tsGT: Stochastic Time Series Modeling With Transformercited by 1
  3. 2025Filling the Missings: Spatiotemporal Data Imputation by Conditional Diffusioncited by 1
  4. 2026Electricity Price Forecasting: Bridging Linear Models, Neural Networks and Online Learningcited by 1
  5. 2026Foundation models for electricity price forecasting and battery arbitrage: Can they replace market-specific forecasting models?cited by 1
  6. 2024Efficient pooling of predictions via kernel embeddingscited by 0
  7. 2026ConquerNet: Convolution-Smoothed Quantile ReLU Neural Networks with Minimax Guaranteescited by 0
  8. 2026SPECTRA: State-Space Exogenous Context and Temporal-Frequency Resolution Architecture for Probabilistic Energy Forecastingcited by 0
  9. 2026TEMPER: Temporal Encoder-Masked Probabilistic Ensemble Regressor for Time-Series Forecastingcited by 0