Decentralized Inference for Spatial Data Using Low-Rank Models

Music City Center 

Advancements in information technology have enabled the generation of massive spatial datasets, necessitating scalable distributed methods. Centralized frameworks are prone to vulnerabilities such as single-point failures and communication bottlenecks. This paper introduces a decentralized framework for parameter inference in spatial low-rank models to address these limitations. A key challenge stems from spatial dependence among observations, which prevents the log-likelihood from being expressed as a summation-a critical requirement for decentralized optimization. To overcome this, we propose a novel objective function leveraging the evidence lower bound, facilitating the application of decentralized optimization techniques. Our approach integrates block descent with multi-consensus and dynamic consensus averaging for effective parameter optimization. We prove the new objective's convexity near true parameters, ensuring convergence. Additionally, we establish theoretical results on the consistency and asymptotic normality of the estimator for spatial low-rank models. Extensive simulations and real-world experiments confirm the framework's robustness and scalability.

Block descent method

Dynamic consensus averaging

Evidence lower bound

Multi-consensus

Spatial dependence 

Section on Statistics and the Environment