用图像模型加速非平稳空间数据的参数估计
LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data
- 将空间参数构造成网格图像，用图像到图像网络直接预测
- 在复杂非平稳模型上实现更快更准的参数推断
- 适合处理高维空间数据的科研与工程人员
在许多应用中，需对少量空间分布的随机变量（'场'）拟合参数化统计模型。然而，使用最大似然估计（MLE）进行参数推断在大规模非平稳场中计算成本过高。因此，近期许多工作训练神经网络，直接以空间场为输入估计参数，完全跳过MLE。本文聚焦一类流行的参数化空间自回归（SAR）模型。我们提出一个简单但关键的观察：由于SAR参数可排列成规则网格，输入（空间场）和输出（模型参数）均可视为图像。基于此，我们证明图像到图像（I2I）网络能实现前所未有的复杂度下，对非平稳SAR模型的快速且更精确的参数估计。
原文摘要 · Abstract (English)
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.
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