用基图拉斯索对大规模高维非平稳空间数据建模
Modeling massive highly-multivariate nonstationary spatial data with the basis graphical lasso
AI总结：
本文提出基图拉斯索框架，将多尺度基函数与高斯图模型结合，以线性复杂度对高维非平稳空间过程建模，并在含40个空间过程的大型气候集合上验证了方法。
摘要：
我们提出了一个新的高维空间过程建模框架，该框架综合了近期多尺度与谱方法以及图模型的思想。基图拉斯索将一个单变量高斯过程写成基函数的线性组合，其权重为高斯图向量的分量，该图通过优化带 $\ell_1$ 惩罚的似然来估计。本文将这一设定扩展到多变量高斯过程，其中基函数由高斯图向量加权。我们构建了一个模型，其中基函数表示不同的分辨率层级，并假设每一层的图向量相互独立。使用正交基可在空间位置数量、基函数数量和实现次数上实现线性复杂度和线性内存占用。额外的融合惩罚鼓励在多级图模型中产生简约的条件独立结构。我们在美国国家大气研究中心社区大气模式的一个大型气候集合上展示了我们的方法，该集合涉及 40 个空间过程。
英文摘要：
We propose a new modeling framework for highly-multivariate spatial processes that synthesizes ideas from recent multiscale and spectral approaches with graphical models. The basis graphical lasso writes a univariate Gaussian process as a linear combination of basis functions weighted with entries of a Gaussian graphical vector whose graph is estimated from optimizing an $\ell_1$ penalized likelihood. This paper extends the setting to a multivariate Gaussian process where the basis functions are weighted with Gaussian graphical vectors. We motivate a model where the basis functions represent different levels of resolution and the graphical vectors for each level are assumed to be independent. Using an orthogonal basis grants linear complexity and memory usage in the number of spatial locations, the number of basis functions, and the number of realizations. An additional fusion penalty encourages a parsimonious conditional independence structure in the multilevel graphical model. We illustrate our method on a large climate ensemble from the National Center for Atmospheric Research's Community Atmosphere Model that involves 40 spatial processes.
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