通过非凸正则化估计稀疏协方差矩阵

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Xin Wang , Lingchen Kong , Liqun Wang
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引用次数: 0

摘要

高维稀疏协方差矩阵估计是多元分析中的基础和重要问题之一,在许多领域都有广泛的应用。本文提出了一种通过求解非凸正则优化问题进行稀疏协方差矩阵估计的新方法。我们建立了所提估计器的渐近特性,并开发了一种多级凸松弛方法来找到有效的估计器。多阶段凸松弛法保证了所生成序列的任何累积点都是非凸优化的一阶静止点。此外,在一些规则性条件下,还推导出了多阶段凸松弛法前两阶段估计器的误差边界。数值结果表明,我们的估计器优于最先进的估计器,并且在有效的前提下具有高度的稀疏性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Estimation of sparse covariance matrix via non-convex regularization

Estimation of high-dimensional sparse covariance matrix is one of the fundamental and important problems in multivariate analysis and has a wide range of applications in many fields. This paper presents a novel method for sparse covariance matrix estimation via solving a non-convex regularization optimization problem. We establish the asymptotic properties of the proposed estimator and develop a multi-stage convex relaxation method to find an effective estimator. The multi-stage convex relaxation method guarantees any accumulation point of the sequence generated is a first-order stationary point of the non-convex optimization. Moreover, the error bounds of the first two stage estimators of the multi-stage convex relaxation method are derived under some regularity conditions. The numerical results show that our estimator outperforms the state-of-the-art estimators and has a high degree of sparsity on the premise of its effectiveness.

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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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