We propose a new approach for the modeling large datasets of nonstationary spatial processes that combines a latent low rank process and a sparse covariance model. The low rank component coefficients are endowed with a flexible graphical Gaussian Markov random field model. The utilization of a low rank and compactly-supported covariance structure combines the full-scale approximation and the basis graphical lasso; we term this new approach the full-scale basis graphical lasso (FSBGL). Estimation employs a graphical lasso-penalized likelihood, which is optimized using a difference-of-convex scheme. We illustrate the proposed approach on synthetic fields as well as with a challenging high-resolution simulation dataset of the thermosphere. In a comparison against state-of-the-art spatial models, the FSBGL performs better at capturing salient features of the thermospheric temperature fields, even with limited available training data.

翻译：我们提出一种新方法，用于对大规模非平稳空间过程数据集进行建模，该方法结合了潜在低秩过程与稀疏协方差模型。低秩分量系数采用灵活的图高斯马尔可夫随机场模型。通过利用低秩且紧支撑的协方差结构，我们将全尺度近似与基图拉索相结合；我们将这种新方法称为全尺度基图拉索(FSBGL)。估计过程采用带图拉索惩罚的似然函数，并通过差分凸优化方案进行优化。我们在合成场以及具有挑战性的高层大气高分辨率模拟数据集上展示了所提出方法的效果。与最先进的空间模型相比，即使训练数据有限，FSBGL在捕捉热层温度场显著特征方面表现更优。