Multi-resolution filters via linear projection for large spatio-temporal datasets
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917982090821632 |
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| author | Hirano, Toshihiro Ishihara, Tsunehiro |
| author_facet | Hirano, Toshihiro Ishihara, Tsunehiro |
| contents | Advances in compact sensing devices mounted on satellites have facilitated the collection of large spatio-temporal datasets with coordinates. Since such datasets are often incomplete and noisy, it is useful to create the prediction surface of a spatial field. To this end, we consider an online filtering inference by using the Kalman filter based on linear Gaussian state-space models. However, the Kalman filter is impractically time-consuming when the number of locations in spatio-temporal datasets is large. To address this problem, we propose a multi-resolution filter via linear projection (MRF-lp), a fast computation method for online filtering inference. In the MRF-lp, by carrying out a multi-resolution approximation via linear projection (MRA-lp), the forecast covariance matrix can be approximated while capturing both the large- and small-scale spatial variations. As a result of this approximation, our proposed MRF-lp preserves a block-sparse structure of some matrices appearing in the MRF-lp through time, which leads to the scalability of this algorithm. Additionally, we discuss extensions of the MRF-lp to a nonlinear and non-Gaussian case. Simulation studies and real data analysis for total precipitable water vapor demonstrate that our proposed approach performs well compared with the related methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05315 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multi-resolution filters via linear projection for large spatio-temporal datasets Hirano, Toshihiro Ishihara, Tsunehiro Methodology Computation Advances in compact sensing devices mounted on satellites have facilitated the collection of large spatio-temporal datasets with coordinates. Since such datasets are often incomplete and noisy, it is useful to create the prediction surface of a spatial field. To this end, we consider an online filtering inference by using the Kalman filter based on linear Gaussian state-space models. However, the Kalman filter is impractically time-consuming when the number of locations in spatio-temporal datasets is large. To address this problem, we propose a multi-resolution filter via linear projection (MRF-lp), a fast computation method for online filtering inference. In the MRF-lp, by carrying out a multi-resolution approximation via linear projection (MRA-lp), the forecast covariance matrix can be approximated while capturing both the large- and small-scale spatial variations. As a result of this approximation, our proposed MRF-lp preserves a block-sparse structure of some matrices appearing in the MRF-lp through time, which leads to the scalability of this algorithm. Additionally, we discuss extensions of the MRF-lp to a nonlinear and non-Gaussian case. Simulation studies and real data analysis for total precipitable water vapor demonstrate that our proposed approach performs well compared with the related methods. |
| title | Multi-resolution filters via linear projection for large spatio-temporal datasets |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2401.05315 |