Geo-spatio-temporal data are valuable for a broad range of applications including traffic forecasting, weather prediction, detection of epidemic outbreaks, and crime monitoring. Data driven approaches to these problems must address several fundamental challenges such as handling the %The two we focus on are the importance ofgeo-spatio-temporal relationships and extreme events. Another recent technological shift has been the success of deep learning especially in applications such as computer vision, speech recognition, and natural language processing. In this work, we argue that deep learning is a promising approach for many geo-spatio-temporal problems and highlight how it can be used to address the challenges of modeling geo-spatio-temporal relationships and extremes. Though previous research has established techniques for modeling spatio-temporal relationships, these approaches are often limited to gridded spatial data with fixed-length feature vectors and considered only spatial relationships among the features, while ignoring the relationships among model parameters.We begin by describing how the spatial and temporal relationships for non-gridded spatial data can be modeled simultaneously by coupling the graph convolutional network with a long short-term memory (LSTM) network. Unlike previous research, our framework treats the adjacency matrix associated with the spatial data as a model parameter that can be learned from data, with constraints on its sparsity and rank to reduce the number of estimated parameters.Further, we show that the learned adjacency matrix may reveal useful information about the dominant spatial relationships that exist within the data. Second, we explore the varieties of spatial relationships that may exist in a geo-spatial prediction task. Specifically, we distinguish between spatial relationships among predictors and the spatial relationships among model parameters at different locations. We demonstrate an approach for modeling spatial dependencies among model parameters using graph convolution and provide guidance on when convolution of each type can be effectively applied. We evaluate our proposed approach on a climate downscaling and weather prediction tasks. Next, we introduce DeepGPD, a novel deep learning framework for predicting the distribution of geo-spatio-temporal extreme events. We draw on research in extreme value theory and use the generalized Pareto distribution (GPD) to model the distribution of excesses over a threshold. The GPD is integrated into our deep learning framework to learn the distribution of future excess values while incorporating the geo-spatio-temporal relationships present in the data. This requires a novel reparameterization of the GPD to ensure that its constraints are satisfied by the outputs of the neural network. We demonstrate the effectiveness of our proposed approach on a real-world precipitation data set. DeepGPD also employs a deep set architecture to handle the variable-sized feature sets corresponding to excess values from previous time steps as its predictors. Finally, we extend the DeepGPD formulation to simultaneously predict the distribution of extreme events and accurately infer their point estimates. Doing so requires modeling the full distribution of the data not just its extreme values. We propose DEMM, a deep mixture model for modeling the distribution of both excess and non-excess values. To ensure the point estimation of DEMM is a feasible value, new constraints on the output of the neural network are introduced, which requires a new reparameterization of the model parameters of the GPD. We conclude by discussing possibilities for further research at the intersection of deep learning and geo-spatio-temporal data.
Read
