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Multiple Matrix Gaussian Graphs Estimation.
The Journal of the Royal Statistical Society, Series B (Statistical Methodology) ( IF 5.8 ) Pub Date : 2018-12-07 , DOI: 10.1111/rssb.12278
Yunzhang Zhu 1 , Lexin Li 2
Affiliation  

Matrix-valued data, where the sampling unit is a matrix consisting of rows and columns of measurements, are emerging in numerous scientific and business applications. Matrix Gaussian graphical model is a useful tool to characterize the conditional dependence structure of rows and columns. In this article, we employ nonconvex penalization to tackle the estimation of multiple graphs from matrix-valued data under a matrix normal distribution. We propose a highly efficient nonconvex optimization algorithm that can scale up for graphs with hundreds of nodes. We establish the asymptotic properties of the estimator, which requires less stringent conditions and has a sharper probability error bound than existing results. We demonstrate the efficacy of our proposed method through both simulations and real functional magnetic resonance imaging analyses.

中文翻译:

多重矩阵高斯图估计。

在许多科学和商业应用中都出现了矩阵值数据,其中采样单位是由行和列的测量组成的矩阵。矩阵高斯图形模型是表征行和列的条件依存结构的有用工具。在本文中,我们采用非凸罚分法来解决在矩阵正态分布下根据矩阵值数据对多个图形的估计。我们提出了一种高效的非凸优化算法,该算法可以扩展到具有数百个节点的图。我们建立了估计器的渐近性质,它要求的条件不那么严格,并且比现有结果具有更大的概率误差范围。我们通过仿真和实际功能磁共振成像分析证明了我们提出的方法的有效性。
更新日期:2019-11-01
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