Influenced mixed moving average fields are a versatile modeling class for spatio-temporal data. However, their predictive distribution is not generally accessible. Under this modeling assumption, we define a novel theory-guided machine learning approach that employs a generalized Bayesian algorithm to make predictions. We employ a Lipschitz predictor, for example, a linear model or a feed-forward neural network, and determine a randomized estimator by minimizing a novel PAC Bayesian bound for data serially correlated along a spatial and temporal dimension. Performing causal future predictions is a highlight of our methodology as its potential application to data with short and long-range dependence. We conclude by showing the performance of the learning methodology in an example with linear predictors and simulated spatio-temporal data from an STOU process.

翻译：受混合移动平均场影响是一类通用的时空数据建模方法，但其预测分布通常难以直接获取。基于该建模假设，我们定义了一种新颖的理论引导机器学习方法，通过采用广义贝叶斯算法进行预测。我们使用Lipschitz预测器（例如线性模型或前馈神经网络），并通过最小化针对时空序列相关数据的新型PAC贝叶斯界来确定随机化估计量。该方法的一个亮点是能够对具有短程和长程依赖性的数据进行因果未来预测。最后，我们通过线性预测器示例及来自STOU过程的模拟时空数据展示了该学习方法的性能。