A discrete spatial lattice can be cast as a network structure over which spatially-correlated outcomes are observed. A second network structure may also capture similarities among measured features, when such information is available. Incorporating the network structures when analyzing such doubly-structured data can improve predictive power, and lead to better identification of important features in the data-generating process. Motivated by applications in spatial disease mapping, we develop a new doubly regularized regression framework to incorporate these network structures for analyzing high-dimensional datasets. Our estimators can be easily implemented with standard convex optimization algorithms. In addition, we describe a procedure to obtain asymptotically valid confidence intervals and hypothesis tests for our model parameters. We show empirically that our framework provides improved predictive accuracy and inferential power compared to existing high-dimensional spatial methods. These advantages hold given fully accurate network information, and also with networks which are partially misspecified or uninformative. The application of the proposed method to modeling COVID-19 mortality data suggests that it can improve prediction of deaths beyond standard spatial models, and that it selects relevant covariates more often.

翻译：离散空间格网可视为观测空间相关结果的网络结构。当此类信息可用时，第二种网络结构也可用于捕捉测量特征间的相似性。在分析此类双重结构数据时纳入网络结构，能够提升预测能力，并更好地识别数据生成过程中的重要特征。受空间疾病制图应用的启发，我们开发了一种新的双重正则化回归框架，以纳入这些网络结构来分析高维数据集。我们的估计量可通过标准凸优化算法轻松实现。此外，我们描述了获得模型参数的渐近有效置信区间与假设检验的程序。实证研究表明，与现有高维空间方法相比，我们的框架能提供更优的预测精度与推断效能。这些优势在给定完全准确网络信息时成立，在网络部分误设或信息不足时同样有效。将所提方法应用于COVID-19死亡率数据建模表明，该方法能超越标准空间模型改进死亡预测，并更频繁地选择相关协变量。