Imma Valentina Curato

Imma Valentina Curato, Orkun Furat, Lorenzo Proietti et al.

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.

Leonardo Bardi, Imma Valentina Curato, Lorenzo Proietti

We employ stochastic feed-forward neural networks with Gaussian-distributed weights to determine a probabilistic forecast for spatio-temporal raster datasets. The networks are trained using MMAF-guided learning, a generalized Bayesian methodology in which the observed data are preprocessed using an embedding designed to produce a low-dimensional representation that captures their dependence and causal structure. The design of the embedding is theory-guided by the assumption that a spatio-temporal Ornstein-Uhlenbeck process with finite second-order moments generates the observed data. The trained networks, in inference mode, are then used to generate ensemble forecasts by applying different initial conditions at different horizons. Experiments conducted on both synthetic and real data demonstrate that our forecasts remain calibrated across multiple time horizons. Moreover, we show that on such data, simple feed-forward architectures can achieve performance comparable to, and in some cases better than, convolutional or diffusion deep learning architectures used in probabilistic forecasting tasks.