Statistical Deep Learning for Spatial and Spatio-Temporal Data
This is an incremental review for researchers in statistics and machine learning interested in combining statistical and deep learning approaches for spatial and spatio-temporal data.
This review tackles the problem of modeling spatial and spatio-temporal data by presenting an overview of traditional methods and focusing on hybrid models that integrate statistical modeling with deep neural networks to leverage the strengths of both paradigms, without providing specific numerical results.
Deep neural network models have become ubiquitous in recent years, and have been applied to nearly all areas of science, engineering, and industry. These models are particularly useful for data that have strong dependencies in space (e.g., images) and time (e.g., sequences). Indeed, deep models have also been extensively used by the statistical community to model spatial and spatio-temporal data through, for example, the use of multi-level Bayesian hierarchical models and deep Gaussian processes. In this review, we first present an overview of traditional statistical and machine learning perspectives for modeling spatial and spatio-temporal data, and then focus on a variety of hybrid models that have recently been developed for latent process, data, and parameter specifications. These hybrid models integrate statistical modeling ideas with deep neural network models in order to take advantage of the strengths of each modeling paradigm. We conclude by giving an overview of computational technologies that have proven useful for these hybrid models, and with a brief discussion on future research directions.