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.

翻译：概率预测依赖历史观测数据为未来结果提供概率分布，通常通过评分规则依据实际观测值进行评估。本文采用生成神经网络进行概率预测，该网络通过变换潜变量中的抽样来参数化高维空间上的分布。生成网络通常采用对抗式框架进行训练。与此不同，我们提出训练生成网络以最小化感兴趣现象的时间序列上的预测序列（或序贯）评分规则，这一方法具有吸引力，因为其恰好对应预测系统常规评估的方式。对于某些评分规则而言，无对抗式最小化是可行的；因此，我们的框架避免了由于不稳定的对抗训练导致的繁琐超参数调优和不确定性低估问题，从而实现了生成网络在概率预测中的可靠应用。此外，我们证明了目标函数最小化器在处理依赖数据时的一致性，而对抗训练则假设数据独立。我们在两个混沌动力学模型及全球天气观测基准数据集上进行了仿真研究；对于最后一个案例，我们通过参考相关文献定义了空间数据的评分规则。我们的方法优于现有最先进的对抗式方法，尤其在概率校准方面表现突出，且所需超参数调优更少。