Decentralized Inference for Spatial Data Using Low-Rank Models

TL;DR

This paper introduces a decentralized inference framework for spatial low-rank models that overcomes the limitations of centralized methods by ensuring scalability, robustness, and theoretical guarantees through novel optimization techniques.

Contribution

It proposes a new objective function based on the evidence lower bound, enabling decentralized optimization for spatial data with proven convergence and statistical properties.

Findings

The method is scalable and robust in large spatial datasets.

Theoretical proofs establish estimator consistency and asymptotic normality.

Simulations and real data validate the approach's effectiveness.

Abstract

Advancements in information technology have enabled the creation of massive spatial datasets, driving the need for scalable and efficient computational methodologies. While offering viable solutions, centralized frameworks are limited by vulnerabilities such as single-point failures and communication bottlenecks. This paper presents a decentralized framework tailored for parameter inference in spatial low-rank models to address these challenges. A key obstacle arises from the spatial dependence among observations, which prevents the log-likelihood from being expressed as a summation-a critical requirement for decentralized optimization approaches. To overcome this challenge, we propose a novel objective function leveraging the evidence lower bound, which facilitates the use of decentralized optimization techniques. Our approach employs a block descent method integrated with multi-consensus and dynamic consensus averaging for effective parameter optimization. We prove the convexity of the new objective function in the vicinity of the true parameters, ensuring the convergence of the proposed method. Additionally, we present the first theoretical results establishing the consistency and asymptotic normality of the estimator within the context of spatial low-rank models. Extensive simulations and real-world data experiments corroborate these theoretical findings, showcasing the robustness and scalability of the framework.