Scalable Spatiotemporal Prediction with Bayesian Neural Fields

TL;DR

The BayesNF is introduced, a domain-general statistical model that infers rich spatiotemporal probability distributions for data-analysis tasks including forecasting, interpolation, and variography and delivers improvements on prediction problems from climate and public health data containing tens to hundreds of thousands of measurements.

Abstract

Spatiotemporal datasets, which consist of spatially-referenced time series, are ubiquitous in diverse applications, such as air pollution monitoring, disease tracking, and cloud-demand forecasting. As the scale of modern datasets increases, there is a growing need for statistical methods that are flexible enough to capture complex spatiotemporal dynamics and scalable enough to handle many observations. This article introduces the Bayesian Neural Field (BayesNF), a domain-general statistical model that infers rich spatiotemporal probability distributions for data-analysis tasks including forecasting, interpolation, and variography. BayesNF integrates a deep neural network architecture for high-capacity function estimation with hierarchical Bayesian inference for robust predictive uncertainty quantification. Evaluations against prominent baselines show that BayesNF delivers improvements on prediction problems from climate and public health data containing tens to hundreds of thousands of measurements. Accompanying the paper is an open-source software package (https://github.com/google/bayesnf) that runs on GPU and TPU accelerators through the JAX machine learning platform.

Figures (2)

• Figure 1: Probabilistic graphical model representation of the Bayesian Neural Field. \ref{['fig:network-input']} An example spatiotemporal domain comprised of two spatial coordinates (latitude, longitude) and a daily time coordinate. \ref{['fig:network-structure']} In the probabilistic graphical model, each node denotes a model variable and each edge denotes a direct relationship between a pair of variables. Gray nodes are observed variables and white notes are local latent variables, which are both associated with an observation $Y(\mathbf{s},t)$ at a spatiotemporal coordinate $(\mathbf{s},t)$. Pink nodes are global latent variables (parameters), which are shared across all spatiotemporal coordinates. \ref{['fig:network-output']} Realizations of the spatiotemporal field generated from the BayesNF at four example time points. Satellite basemap source: esri.
• Figure 2: Spatiotemporal datasets analyzed in the empirical evaluation.