Influenced mixed moving average fields are a versatile modeling class for spatio-temporal data. However, their predictive distribution is not generally known. Under this modeling assumption, we define a novel spatio-temporal embedding and a theory-guided machine learning approach that employs a generalized Bayesian algorithm to make ensemble forecasts. We employ Lipschitz predictors and determine fixed-time and any-time PAC Bayesian bounds in the batch learning setting. Performing causal forecast is a highlight of our methodology as its potential application to data with spatial and temporal short and long-range dependence. We then test the performance of our learning methodology by using linear predictors and data sets simulated from a spatio-temporal Ornstein-Uhlenbeck process.

翻译：受混合移动平均场影响的模型是时空数据中一类灵活的建模方式。然而，其预测分布通常并不明确。在此建模假设下，我们定义了一种新型时空嵌入方法，并采用理论引导的机器学习方法，利用广义贝叶斯算法进行集成预测。我们采用Lipschitz预测器，并在批量学习设置中确定了固定时间和任意时间的PAC贝叶斯界限。进行因果预测是我们方法论的一个亮点，因为它具有对具有空间和时间短程及长程依赖性的数据进行潜在应用的优势。最后，我们通过使用线性预测器以及从时空Ornstein-Uhlenbeck过程模拟的数据集来测试我们学习方法的性能。