# Online Learning with Continuous Ranked Probability Score

arXiv: https://arxiv.org/abs/1902.10173 · HTML: https://mlsanity.com/paper/1902.10173/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2019.

## Built on by (most cited first, 6 of 6)

- [Collaborative Multi-Object Tracking with Conformal Uncertainty Propagation](https://mlsanity.com/paper/2303.14346/) (2023)
- [Stochastic Online Convex Optimization. Application to probabilistic time series forecasting](https://mlsanity.com/paper/2102.00729/) (2021)
- [CLEAR: Calibrated Learning for Epistemic and Aleatoric Risk](https://mlsanity.com/paper/2507.08150/) (2025)
- [Probabilistic Self-supervised Learning via Scoring Rules Minimization](https://mlsanity.com/paper/2309.02048/) (2023)
- [Online Aggregation of Probability Forecasts with Confidence](https://mlsanity.com/paper/2109.14309/) (2021)
- [SEMF: Supervised Expectation-Maximization Framework for Predicting Intervals](https://mlsanity.com/paper/2405.18176/) (2024)

## Abstract (arXiv)

Probabilistic forecasts in the form of probability distributions over future events have become popular in several fields of statistical science. The dissimilarity between a probability forecast and an outcome is measured by a loss function (scoring rule). Popular example of scoring rule for continuous outcomes is the continuous ranked probability score (CRPS). We consider the case where several competing methods produce online predictions in the form of probability distribution functions. In this paper, the problem of combining probabilistic forecasts is considered in the prediction with expert advice framework. We show that CRPS is a mixable loss function and then the time independent upper bound for the regret of the Vovk's aggregating algorithm using CRPS as a loss function can be obtained. We present the results of numerical experiments illustrating the proposed methods.