论文标题
Sylvester图形拉索（Syglasso）
The Sylvester Graphical Lasso (SyGlasso)
论文作者
论文摘要
本文介绍了Sylvester图形拉索（Syglasso），该拉索（Syglasso）捕获了张量值数据中存在的多路依赖性。该模型基于定义生成模型的Sylvester方程。提出的模型补充了张量图图形拉索（Greenewald等，2019），该拉索通过提供了一种替代的kronecker sum模型，该模型构成了逆协方差矩阵的Kronecker Sum模型，该模型是生成且可解释的。采用了一种点向回归方法来估计变量之间的条件独立关系。建立了该方法的统计收敛性，并提供了经验研究以证明有意义的条件依赖图的恢复。我们将Syglasso应用于脑电图（EEG）研究，以比较酒精和非酒精受试者的大脑连通性。我们证明我们的模型可以同时估计大脑连接性及其时间依赖性。
This paper introduces the Sylvester graphical lasso (SyGlasso) that captures multiway dependencies present in tensor-valued data. The model is based on the Sylvester equation that defines a generative model. The proposed model complements the tensor graphical lasso (Greenewald et al., 2019) that imposes a Kronecker sum model for the inverse covariance matrix by providing an alternative Kronecker sum model that is generative and interpretable. A nodewise regression approach is adopted for estimating the conditional independence relationships among variables. The statistical convergence of the method is established, and empirical studies are provided to demonstrate the recovery of meaningful conditional dependency graphs. We apply the SyGlasso to an electroencephalography (EEG) study to compare the brain connectivity of alcoholic and nonalcoholic subjects. We demonstrate that our model can simultaneously estimate both the brain connectivity and its temporal dependencies.
