文章基本信息

标题：Compressed Covariance Estimation with Automated Dimension Learning
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作者：Gautam Sabnis ; Gautam Sabnis ; Debdeep Pati 等
期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2018
页码：1-16
DOI：10.1007/s13171-018-0134-x
出版社：Indian Statistical Institute
摘要：We propose a method for estimating a covariance matrix that can be represented as a sum of a low-rank matrix and a diagonal matrix. The proposed method compresses high-dimensional data, computes the sample covariance in the compressed space, and lifts it back to the ambient space via a decompression operation. A salient feature of our approach relative to existing literature on combining sparsity and low-rank structures in covariance matrix estimation is that we do not require the low-rank component to be sparse. A principled framework for estimating the compressed dimension using Stein’s Unbiased Risk Estimation theory is demonstrated. Experimental simulation results demonstrate the efficacy and scalability of our proposed approach..
关键词：Compressed sensing ; Dimension reduction ; Low;rank ; Factor model ; Spiked covariance models ; SURE