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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2502.00309 |
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| _version_ | 1866929705597272064 |
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| author | Shi, Jianwei Abdulah, Sameh Sun, Ying Genton, Marc G. |
| author_facet | Shi, Jianwei Abdulah, Sameh Sun, Ying Genton, Marc G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00309 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decentralized Inference for Spatial Data Using Low-Rank Models Shi, Jianwei Abdulah, Sameh Sun, Ying Genton, Marc G. Machine Learning Computation Methodology 62M30 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. |
| title | Decentralized Inference for Spatial Data Using Low-Rank Models |
| topic | Machine Learning Computation Methodology 62M30 |
| url | https://arxiv.org/abs/2502.00309 |