空气质量数据的函数型高斯图回归模型
Functional Gaussian Graphical Regression Models For Air Quality Data
AI总结：
针对大气化学物质空间相互作用分析，提出函数型高斯图回归模型及双重惩罚估计量，并引入联合Kullback-Leibler交叉验证，有效解决了函数型响应与协变量相关性评估难题。
摘要：
函数型数据描述了广泛的过程，例如生长曲线和光谱吸收。在本研究中，我们分析了来自In-service Aircraft for a Global Observing System的空气污染数据，重点关注大气中化学物质之间的空间相互作用及其对气象条件的依赖性。这需要使用函数回归，其中响应变量和协变量都是在对流层中演化的函数对象。评估响应变量与协变量之间的函数相关性以及多变量响应函数的相关性可能具有挑战性。我们通过引入函数型高斯图回归模型来解决这些挑战，将条件高斯图模型扩展到部分可分函数。为了估计该模型，我们提出了一种双重惩罚估计量。此外，我们提出了一种针对图估计量的Kullback-Leibler交叉验证的新颖改编，当总体存在一个或多个子组时，该验证会考虑精度和回归矩阵，称为联合Kullback-Leibler交叉验证。模型性能的评估在Kullback-Leibler散度和图恢复能力方面进行。
英文摘要：
Functional data describe a wide range of processes, such as growth curves and spectral absorption. In this study, we analyze air pollution data from the In-service Aircraft for a Global Observing System, focusing on the spatial interactions among chemicals in the atmosphere and their dependence on meteorological conditions. This requires functional regression, where both response and covariates are functional objects evolving over the troposphere. Evaluating both the functional relatedness between the response and covariates and the relatedness of a multivariate response function can be challenging. We propose a solution to these challenges by introducing a functional Gaussian graphical regression model, extending conditional Gaussian graphical models to partially separable functions. To estimate the model, we propose a doubly-penalized estimator. Additionally, we present a novel adaptation of Kullback-Leibler cross-validation tailored for graph estimators which accounts for precision and regression matrices when the population presents one or more sub-groups, named joint Kullback-Leibler cross-validation. Evaluation of model performance is done in terms of Kullback-Leibler divergence and graph recovery power.
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