Spatio-Temporal Functional Neural Networks
This work addresses spatio-temporal regression problems, which are important for applications like meteorology, though it appears incremental as it builds on existing FNN models.
The authors tackled spatio-temporal regression by proposing two novel extensions of Functional Neural Networks (FNNs) to better handle spatial and temporal dependencies, demonstrating their effectiveness in simulations and applying them to precipitation prediction in meteorology.
Explosive growth in spatio-temporal data and its wide range of applications have attracted increasing interests of researchers in the statistical and machine learning fields. The spatio-temporal regression problem is of paramount importance from both the methodology development and real-world application perspectives. Given the observed spatially encoded time series covariates and real-valued response data samples, the goal of spatio-temporal regression is to leverage the temporal and spatial dependencies to build a mapping from covariates to response with minimized prediction error. Prior arts, including the convolutional Long Short-Term Memory (CovLSTM) and variations of the functional linear models, cannot learn the spatio-temporal information in a simple and efficient format for proper model building. In this work, we propose two novel extensions of the Functional Neural Network (FNN), a temporal regression model whose effectiveness and superior performance over alternative sequential models have been proven by many researchers. The effectiveness of the proposed spatio-temporal FNNs in handling varying spatial correlations is demonstrated in comprehensive simulation studies. The proposed models are then deployed to solve a practical and challenging precipitation prediction problem in the meteorology field.