LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918457467994112 |
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| author | Sikorski, Antony Ivanitskiy, Michael Lenssen, Nathan Nychka, Douglas McKenzie, Daniel |
| author_facet | Sikorski, Antony Ivanitskiy, Michael Lenssen, Nathan Nychka, Douglas McKenzie, Daniel |
| contents | In many applications, we wish to fit a parametric statistical model to a small ensemble of spatially distributed random variables ('fields'). However, parameter inference using maximum likelihood estimation (MLE) is computationally prohibitive, especially for large, non-stationary fields. Thus, many recent works train neural networks to estimate parameters given spatial fields as input, sidestepping MLE completely. In this work we focus on a popular class of parametric, spatially autoregressive (SAR) models. We make a simple yet impactful observation; because the SAR parameters can be arranged on a regular grid, both inputs (spatial fields) and outputs (model parameters) can be viewed as images. Using this insight, we demonstrate that image-to-image (I2I) networks enable faster and more accurate parameter estimation for a class of non-stationary SAR models with unprecedented complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09803 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data Sikorski, Antony Ivanitskiy, Michael Lenssen, Nathan Nychka, Douglas McKenzie, Daniel Machine Learning In many applications, we wish to fit a parametric statistical model to a small ensemble of spatially distributed random variables ('fields'). However, parameter inference using maximum likelihood estimation (MLE) is computationally prohibitive, especially for large, non-stationary fields. Thus, many recent works train neural networks to estimate parameters given spatial fields as input, sidestepping MLE completely. In this work we focus on a popular class of parametric, spatially autoregressive (SAR) models. We make a simple yet impactful observation; because the SAR parameters can be arranged on a regular grid, both inputs (spatial fields) and outputs (model parameters) can be viewed as images. Using this insight, we demonstrate that image-to-image (I2I) networks enable faster and more accurate parameter estimation for a class of non-stationary SAR models with unprecedented complexity. |
| title | LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.09803 |