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:混合移动平均场是时空数据的一种多功能建模方法。然而,它们的预测分布通常不可取得。在这种建模假设下,我们定义了一种新颖的理论引导机器学习方法,使用广义贝叶斯算法进行预测。我们采用Lipschitz预测器,例如线性模型或前馈神经网络,并通过最小化新的PAC贝叶斯界限来确定随机估计器,以处理沿空间和时间维度序列相关的数据。这种方法的一个亮点是进行因果未来预测,因为它的潜在应用于具有短期和长期依赖性的数据。我们最后通过展示线性预测器和模拟的STOU过程的时空数据示例来展示学习方法的性能。