Mixed moving average field guided learning for spatio-temporal data

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.