Probabilistic Machine Learning Methods for Spatio-Temporal Data

This dissertation presents multiple novel methodological advancements in the realm of machine learning (ML) for spatio-temporal data applications. Traditional machine learning approaches typically have difficultly producing both accurate point predictions and adequate uncertainty quantification for these data, especially in instances where the data themselves are sampled at a fine temporal scale. This is due to the fact that inference on these complex ML models is notably difficult and can impose a significant computational burden. The challenge of forecasting spatio-temporal data is further heightened when attempting to ensure the forecast themselves obey any known physical laws which dictate or influence the underlying data structure. We explore the current challenges in properly quantifying the uncertainty of forecasts for spatio-temporal data applications stemming from contemporary ML models. Methods are introduced to not only calibrate the uncertainty estimates such that proper coverage is achieved but also so there is a realistic expansion of the uncertainty through time. These contemporary ML models are also adapted such that the physical processes present throughout that data are used to inform the learning procedures, so that the forecasts themselves are influenced to be more physically compliant. We demonstrate the power in combining ML models in an ensemble to improve model accuracy in predicting nonstationary, complex temporal data. Finally, a general comparison is made to explore the benefits and drawbacks of ML approaches to time-series forecasting versus the popular and standard statistical approaches, and as a guide to explain how these newfound advanced ML modelling techniques are not necessarily meant to act as a universal best approach for prediction and forecasting.