Statistical Deep Learning for Spatial and Spatiotemporal Data

Abstract

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 spatiotemporal data through, for example, the use of multilevel 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 spatiotemporal 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.

Lake Water Temperature Modeling in an Era of Climate Change: Data Sources, Models, and Future Prospects

“…The boundary between statistical models and ML is a topic of current debate (see e.g., Bzdok, 2017; Bzdok et al., 2018; Wikle & Zammit‐Mangion, 2023), and one may consider the two types of models belonging to the same macro‐group. The main difference between classical statistics and ML methods can be found in the degree of automation (which is lower for statistical models), complexity, and in the number of assumptions that are needed to solve a problem (which is higher for statistical models).…”

“…The main difference between classical statistics and ML methods can be found in the degree of automation (which is lower for statistical models), complexity, and in the number of assumptions that are needed to solve a problem (which is higher for statistical models). Deep learning methods are generally regarded as a subset of ML, and have been combined with both statistical models (Shlezinger et al., 2023; Wikle & Zammit‐Mangion, 2023) and physical models (Read et al., 2019; Reichstein et al., 2019; Y. Zhu et al., 2023). Deep learning models have limited assumptions on the data and processes that are to be modeled, and can use a large amount of information.…”

Fast parameter estimation of generalized extreme value distribution using neural networks

“…Motivated by recent advancements in applying deep learning algorithms to extreme events, as discussed earlier, and inspired by the successful utilization of NNs for time series and spatial data, as evidenced in papers such as Cremanns and Roos (2017), Gerber and Nychka (2021), Majumder et al (2022), and Wikle and Zammit-Mangion (2023), our research introduces a novel estimation method. In this work, we present a new estimation method that utilizes a deep NN to fit univariate GEV distributions to extreme events.…”

An Approach to Data Modeling via Temporal and Spatial Alignment

“…Recently, deep neural networks have also been considered for use in spatial relationships. Reference [23] provided an overview of traditional statistical and machine learning perspectives for modeling spatial and spatiotemporal data, and then focused on a variety of hybrid models that have recently been developed for latent process, data, and parameter specifications. Reference [24] provided a comprehensive overview of methods to analyze deep neural networks and an insight as to how those interpretable and explainable methods help us to understand time-series data.…”