Graph-Guided Banding of the Covariance Matrix
Graph-Guided Banding of the Covariance Matrix
复制标题
协方差矩阵的图形引导分带
DOI：
10.1080/01621459.2018.1442720
复制
发表时间：
2018
影响因子：
3.7
通讯作者：
Bien, Jacob
中科院分区：
文献类型：
--
作者：
Bien, Jacob
正则化已经成为在高维环境下开发协方差矩阵的可靠估计器的主要工具。为了抑制维度灾难，许多方法假定总体协方差(或逆协方差)矩阵是稀疏的，而不对所需的稀疏模式进行特定的结构性假设。一种高度相关但互补的文献研究了被测量变量具有已知顺序的特定设置，在这种情况下，通常假设为带状总体矩阵。虽然带状方法在概念上和计算上都比要求“无模式稀疏”更容易，但它只适用于非常特定的情况(例如，当数据是随时间或一维空间进行测量的时候)。这项工作提出了带状概念的推广，极大地扩展了带状估计量应用的问题范围。我们开发的凸正则化子占据了前一种“无模式稀疏”方法和后一种依赖于已知有序之间的广泛的中间地带。我们的框架定义了关于测量变量的已知图形的带状。这样的图在不同的情况下都是可用的，我们提供了两个新估计器的理论、计算和应用处理。一个名为GGB的R包实现了这些新方法。这篇文章的补充材料可以在网上找到。
Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse covariance) matrix is sparse, while making no particular structural assumptions on the desired pattern of sparsity. A highly-related, yet complementary, literature studies the specific setting in which the measured variables have a known ordering, in which case a banded population matrix is often assumed. While the banded approach is conceptually and computationally easier than asking for “patternless sparsity,” it is only applicable in very specific situations (such as when data are measured over time or one-dimensional space). This work proposes a generalization of the notion of bandedness that greatly expands the range of problems in which banded estimators apply. We develop convex regularizers occupying the broad middle ground between the former approach of “patternless sparsity” and the latter reliance on having a known ordering. Our framework defines bandedness with respect to a known graph on the measured variables. Such a graph is available in diverse situations, and we provide a theoretical, computational, and applied treatment of two new estimators. An R package, called ggb, implements these new methods. Supplementary materials for this article are available online.
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影响因子：
4.5
作者：
Donoho DL;Gavish M;Johnstone IM
通讯作者：
Johnstone IM
影响因子：
2.7
作者：
Bien, Jacob;Tibshirani, Robert J.
通讯作者：
Tibshirani, Robert J.
影响因子：
4.5
作者：
Cai, Tony;Yuan, Ming
通讯作者：
Yuan, Ming
影响因子：
2.7
作者：
Rothman, Adam J.
通讯作者：
Rothman, Adam J.
DOI：
--
发表时间：
2016
期刊：
影响因子：
--
作者：
J. Bien
通讯作者：
J. Bien