Modeling Large Nonstationary Spatial Data with the Full-Scale Basis Graphical Lasso
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916992176357376 |
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| author | LeDuc, Matthew Kleiber, William Matsuo, Tomoko |
| author_facet | LeDuc, Matthew Kleiber, William Matsuo, Tomoko |
| contents | We propose a new approach for the modeling large datasets of nonstationary spatial processes that combines a latent low rank process and a sparse covariance model. The low rank component coefficients are endowed with a flexible graphical Gaussian Markov random field model. The utilization of a low rank and compactly-supported covariance structure combines the full-scale approximation and the basis graphical lasso; we term this new approach the full-scale basis graphical lasso (FSBGL). Estimation employs a graphical lasso-penalized likelihood, which is optimized using a difference-of-convex scheme. We illustrate the proposed approach on synthetic fields as well as with a challenging high-resolution simulation dataset of the thermosphere. In a comparison against state-of-the-art spatial models, the FSBGL performs better at capturing salient features of the thermospheric temperature fields, even with limited available training data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01318 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modeling Large Nonstationary Spatial Data with the Full-Scale Basis Graphical Lasso LeDuc, Matthew Kleiber, William Matsuo, Tomoko Methodology We propose a new approach for the modeling large datasets of nonstationary spatial processes that combines a latent low rank process and a sparse covariance model. The low rank component coefficients are endowed with a flexible graphical Gaussian Markov random field model. The utilization of a low rank and compactly-supported covariance structure combines the full-scale approximation and the basis graphical lasso; we term this new approach the full-scale basis graphical lasso (FSBGL). Estimation employs a graphical lasso-penalized likelihood, which is optimized using a difference-of-convex scheme. We illustrate the proposed approach on synthetic fields as well as with a challenging high-resolution simulation dataset of the thermosphere. In a comparison against state-of-the-art spatial models, the FSBGL performs better at capturing salient features of the thermospheric temperature fields, even with limited available training data. |
| title | Modeling Large Nonstationary Spatial Data with the Full-Scale Basis Graphical Lasso |
| topic | Methodology |
| url | https://arxiv.org/abs/2505.01318 |