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Estimation of a sparse and spiked covariance matrix

机译:稀疏和尖峰协方差矩阵的估计

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We suggest a method for estimating a covariance matrix that can be represented as a sum of a sparse low-rank matrix and a diagonal matrix. Our formulation is based on penalized quadratic loss, which is a convex problem that can be solved via incremental gradient and proximal method. In contrast to other spiked covariance matrix estimation approaches that are related to principal component analysis and factor analysis, our method has a simple formulation and does not constrain entire rows and columns of the matrix to be zero. We further discuss a penalized entropy loss method that is nevertheless nonconvex and necessitates a majorization-minimization algorithm in combination with the incremental gradient and proximal method. We carry out simulations to demonstrate the finite-sample properties focusing on high-dimensional covariance matrices. Finally, the proposed method is illustrated using a gene expression data set.
机译:我们建议一种估计协方差矩阵的方法,该方差矩阵可以表示为稀疏低秩矩阵和对角矩阵。我们的公式基于惩罚性二次损失,这是一个凸问题,可以通过增量梯度和近端方法解决。与其他与主成分分析和因子分析相关的尖峰协方差矩阵估计方法相反,我们的方法公式简单,不会将矩阵的整个行和列限制为零。我们进一步讨论了一种惩罚熵损失方法,该方法仍然是非凸的,并且需要结合增量梯度和近端方法的主要化-最小化算法。我们进行模拟以展示有限样本属性,重点是高维协方差矩阵。最后,使用基因表达数据集说明了所提出的方法。

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