Mixed moving average field guided learning for spatio-temporal data

TL;DR

This paper introduces a novel machine learning approach for spatio-temporal data based on mixed moving average fields, utilizing a Bayesian ensemble method with theoretical guarantees, tested on simulated Ornstein-Uhlenbeck data.

Contribution

It proposes a new embedding and Bayesian learning framework for mixed moving average fields, enabling causal forecasting with theoretical bounds.

Findings

Effective ensemble forecasts for spatio-temporal data.

Theoretical PAC bounds for the proposed method.

Successful application to Ornstein-Uhlenbeck process simulations.

Abstract

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.