Bayesian Complementary Kernelized Learning for Multidimensional Spatiotemporal Data

TL;DR

This paper introduces Bayesian Complementary Kernelized Learning (BCKL), a scalable probabilistic framework combining low-rank tensor factorization and Gaussian Processes to model complex, nonstationary multidimensional spatiotemporal data effectively.

Contribution

The paper proposes BCKL, a novel framework integrating global low-rank and local Gaussian Process components for efficient modeling of complex spatiotemporal dependencies.

Findings

BCKL outperforms existing models in accuracy and uncertainty estimation.

Effective modeling of both global and local dependencies improves predictive performance.

Validated on synthetic and real-world datasets.

Abstract

Probabilistic modeling of multidimensional spatiotemporal data is critical to many real-world applications. As real-world spatiotemporal data often exhibits complex dependencies that are nonstationary and nonseparable, developing effective and computationally efficient statistical models to accommodate nonstationary/nonseparable processes containing both long-range and short-scale variations becomes a challenging task, in particular for large-scale datasets with various corruption/missing structures. In this paper, we propose a new statistical framework -- Bayesian Complementary Kernelized Learning (BCKL) -- to achieve scalable probabilistic modeling for multidimensional spatiotemporal data. To effectively characterize complex dependencies, BCKL integrates two complementary approaches -- kernelized low-rank tensor factorization and short-range spatiotemporal Gaussian Processes. Specifically, we use a multi-linear low-rank factorization component to capture the global/long-range correlations in the data and introduce an additive short-scale GP based on compactly supported kernel functions to characterize the remaining local variabilities. We develop an efficient Markov chain Monte Carlo (MCMC) algorithm for model inference and evaluate the proposed BCKL framework on both synthetic and real-world spatiotemporal datasets. Our experiment results show that BCKL offers superior performance in providing accurate posterior mean and high-quality uncertainty estimates, confirming the importance of both global and local components in modeling spatiotemporal data.