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# Online Learning with Continuous Ranked Probability Score

*Proceedings of the Eighth Symposium on Conformal and Probabilistic Prediction and Applications*, PMLR 105:163-177, 2019.

#### Abstract

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.