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 use 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：受影响的混合移动平均场是时空数据的一种通用建模类别。然而，其预测分布通常未知。在此建模假设下，我们定义了一种新颖的时空嵌入方法以及一种理论引导的机器学习方法，该方法采用广义贝叶斯算法进行集合预测。我们使用Lipschitz预测器，并在批量学习设定中确定了固定时间和任意时间的PAC贝叶斯界。执行因果预测是我们方法的一个突出特点，因其可潜在应用于具有时空短程与长程依赖性的数据。随后，我们通过使用线性预测器以及从时空Ornstein-Uhlenbeck过程模拟生成的数据集，测试了所提学习方法的性能。