A CRPS Loss for Deep Probabilistic Regression

Probabilistic regression is relevant in highstakes areas such as energy forecasting, financial risk assessment, or healthcare. Deep models that directly output a probability distribution usually use ensembles or frame regression as classification into bins. In contrast, we propose to optimize directly for the Continuous Ranked Probability Score (CRPS), a proper scoring rule for probabilistic predictions. For the flexible histogram-like distributions, the CRPS is differentiable and can be used as the loss function of any deep model. We derive and implement the CRPS loss and showcase its performance against cross-entropy in a solar forecasting application. This new loss enables anyone to easily make any deep regressor probabilistic by simply using the new loss with the same computational cost. Surprisingly, using the CRPS loss provides superior results even when training a deterministic regressor. Code and data available at github.com/franchesoni/differentiable-crps.