Probabilistic Forecasting with Generative Networks via Scoring Rule Minimization

Generative networks are often trained to minimize a statistical divergence between the reference distribution and the generative one in an adversarial setting. Some works trained instead generative networks to minimize Scoring Rules, functions assessing how well the generative distribution matches each training sample individually. We show how the Scoring Rule formulation easily extends to the so-called prequential (predictive-sequential) score, whose minimization allows performing probabilistic forecasting with generative networks. This objective leads to adversarial-free training, therefore easily avoiding uncertainty underestimation due to mode collapse, which is a common issue in the adversarial setting and undesirable for probabilistic forecasting. We provide consistency guarantees for the minimizer of the prequential score and employ that to perform probabilistic forecasting for two chaotic dynamical models and a benchmark dataset of global weather observations. For this last example, we define scoring rules for spatial data by drawing from the relevant literature, with which we obtain better uncertainty quantification with little hyperparameter tuning compared to adversarial training.