Bayesian Complementary Kernelized Learning for Multidimensional Spatiotemporal Data
This work addresses the problem of scalable probabilistic modeling for large-scale spatiotemporal data with complex dependencies, which is critical for real-world applications, though it appears incremental as it combines existing approaches.
The paper tackles the challenge of modeling complex, nonstationary, and nonseparable dependencies in multidimensional spatiotemporal data by proposing the Bayesian Complementary Kernelized Learning (BCKL) framework, which integrates kernelized low-rank tensor factorization and short-range Gaussian Processes to achieve scalable probabilistic modeling with accurate posterior mean and uncertainty estimates.
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.