  Probabilistic forecasting relies on past observations to provide a
probability distribution for a future outcome, which is often evaluated against
the realization using a scoring rule. Here, we perform probabilistic
forecasting with generative neural networks, which parametrize distributions on
high-dimensional spaces by transforming draws from a latent variable.
Generative networks are typically trained in an adversarial framework. In
contrast, we propose to train generative networks to minimize a
predictive-sequential (or prequential) scoring rule on a recorded temporal
sequence of the phenomenon of interest, which is appealing as it corresponds to
the way forecasting systems are routinely evaluated. Adversarial-free
minimization is possible for some scoring rules; hence, our framework avoids
the cumbersome hyperparameter tuning and uncertainty underestimation due to
unstable adversarial training, thus unlocking reliable use of generative
networks in probabilistic forecasting. Further, we prove consistency of the
minimizer of our objective with dependent data, while adversarial training
assumes independence. We perform simulation studies on two chaotic dynamical
models and a benchmark data set of global weather observations; for this last
example, we define scoring rules for spatial data by drawing from the relevant
literature. Our method outperforms state-of-the-art adversarial approaches,
especially in probabilistic calibration, while requiring less hyperparameter
tuning.
