Scalable Spatiotemporally Varying Coefficient Modelling with Bayesian Kernelized Tensor Regression
This work addresses scalability issues in spatial statistics for researchers analyzing large spatiotemporal data, though it is incremental as it builds on existing tensor and Bayesian methods.
The paper tackled the high computational cost of spatiotemporally varying coefficient models for large-scale analyses by proposing Bayesian Kernelized Tensor Regression (BKTR), which reformulates the model as a low-rank tensor regression with Gaussian process priors, achieving superior performance and efficiency in experiments on synthetic and real-world datasets.
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.