Mixed moving average field guided learning for spatio-temporal data
This work addresses forecasting challenges for spatio-temporal data with dependencies, but it is incremental as it builds on existing modeling classes with specific theoretical bounds.
The paper tackled the problem of predicting spatio-temporal data using influenced mixed moving average fields, where the predictive distribution is unknown, by developing a theory-guided machine learning approach with spatio-temporal embeddings and generalized Bayesian algorithms, resulting in fixed-time and any-time PAC Bayesian bounds for ensemble forecasts.
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.