Scalable Spatiotemporally Varying Coefficient Modelling with Bayesian Kernelized Tensor Regression

TL;DR

This paper introduces a scalable Bayesian tensor regression framework for modeling large-scale spatiotemporal data, effectively capturing complex nonstationary patterns with reduced computational costs.

Contribution

It reformulates spatiotemporal varying coefficient models as low-rank tensor regression with Gaussian process priors, enabling efficient analysis of large datasets.

Findings

Outperforms existing methods in accuracy and efficiency

Effectively captures nonstationary spatiotemporal patterns

Demonstrates scalability on real-world datasets

Abstract

As a regression technique in spatial statistics, the spatiotemporally varying coefficient model (STVC) is an important tool for discovering nonstationary and interpretable response-covariate associations over both space and time. However, it is difficult to apply STVC for large-scale spatiotemporal analyses due to its high computational cost. To address this challenge, we summarize the spatiotemporally varying coefficients using a third-order tensor structure and propose to reformulate the spatiotemporally varying coefficient model as a special low-rank tensor regression problem. The low-rank decomposition can effectively model the global patterns of large data sets with a substantially reduced number of parameters. To further incorporate the local spatiotemporal dependencies, we use Gaussian process (GP) priors on the spatial and temporal factor matrices. We refer to the overall framework as Bayesian Kernelized Tensor Regression (BKTR), and kernelized tensor factorization can be considered a new and scalable approach to modeling multivariate spatiotemporal processes with a low-rank covariance structure. For model inference, we develop an efficient Markov chain Monte Carlo (MCMC) algorithm, which uses Gibbs sampling to update factor matrices and slice sampling to update kernel hyperparameters. We conduct extensive experiments on both synthetic and real-world data sets, and our results confirm the superior performance and efficiency of BKTR for model estimation and parameter inference.