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.

翻译：在许多应用中，我们希望将参数化统计模型拟合到空间分布的随机变量（“场”）的小型集合上。然而，使用最大似然估计（MLE）进行参数推断在计算上非常昂贵，特别是对于大型、非平稳的场。因此，许多近期研究训练神经网络，以空间场作为输入来估计参数，从而完全绕过了MLE。在本工作中，我们关注一类流行的参数化空间自回归（SAR）模型。我们提出了一个简单但具有重要影响的观察：由于SAR参数可以排列在规则网格上，输入（空间场）和输出（模型参数）都可以被视为图像。利用这一洞见，我们证明，图像到图像（I2I）网络能够为一类具有空前复杂度的非平稳SAR模型实现更快、更准确的参数估计。