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support recovery of Gaussian Graphical Model with False Discovery Rate Control

Journal of Systems Science & Complexity 2023年第6期36卷 2605-2623页

作者： ZHANG Yuhao LIU Yanhong WANG Zhaojun School of Mathematics and Statistics Jiangsu Normal UniversityXuzhou221116China School of Statistics and Data Science Nankai UniversityTianjin300071China

This paper focuses on the support recovery of the Gaussian graphical model(GGM)with false discovery rate(FDR)*** graceful symmetrized data aggregation(SDA)technique which involves sample splitting,data screening and information pooling is exploited via a node-based way.A matrix of test statistics with symmetry property is constructed and a data-driven threshold is chosen to control the FDR for the support recovery of *** proposed method is shown to control the FDR asymptotically under some mild *** simulation studies and a real-data example demonstrate that it yields a better FDR control while offering reasonable power in most cases.

关键词： False discovery rate Gaussian graphical model support recovery symmetrized data aggregation

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Coherence Based Sufficient Condition for support recovery Using Generalized Orthogonal Matching Pursuit

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Computer Systems Science & Engineering 2023年第5期45卷 2049-2058页

作者： Aravindan Madhavan Yamuna Govindarajan Neelakandan Rajamohan Department of Electronics and Communication Engineering Annamalai UniversityChidambaram608002Tamil NaduIndia School of Electrical Sciences Indian Institute of TechnologyFarmgudiPondaGoaIndia

In an underdetermined system,compressive sensing can be used to recover the support *** algorithms will recover the support vector indices in an iterative *** Orthogonal Matching Pursuit(GOMP)is the generalized form of the Orthogonal Matching Pursuit(OMP)algorithm where a number of indices selected per iteration will be greater than or equal to *** recover the support vector of unknown signal‘x’from the compressed measurements,the restricted isometric property should be satisfied as a sufficient *** the restricted isometric constant is a non-deterministic polynomial-time hardness problem due to that the coherence of the sensing matrix can be used to derive the sufficient condition for support *** this paper a sufficient condition based on the coherence parameter to recover the support vector indices of an unknown sparse signal‘x’using GOMP has been *** derived sufficient condition will recover support vectors of P-sparse signal within‘P’*** recovery guarantee for GOMP is less restrictive,and applies to OMP when the number of selection elements equals *** shows the superior performance of the GOMP algorithm compared with other greedy algorithms.

关键词： Compressed sensing restricted isometric constant generalized orthogonal matching pursuit support recovery recovery guarantee coherence

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Some Results for Exact support recovery of Block Joint Sparse Matrix via Block Multiple Measurement Vectors Algorithm

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Journal of Applied Mathematics and Physics 2023年第4期11卷 1098-1112页

作者： Yingna Pan Pingping Zhang School of Science Chongqing University of Posts and Telecommunications Chongqing China

Block multiple measurement vectors (BMMV) is a reconstruction algorithm that can be used to recover the support of block K-joint sparse matrix X from Y = ΨX + V. In this paper, we propose a sufficient condition for accurate support recovery of the block K-joint sparse matrix via the BMMV algorithm in the noisy case. Furthermore, we show the optimality of the condition we proposed in the absence of noise when the problem reduces to single measurement vector case.

关键词： support recovery Compressed Sensing Block Multiple Measurement Vectors Algorithm Block Restricted Isometry Property

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A stochastic gradient-based two-step sparse identification algorithm for multivariate ARX systems

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Control Theory and Technology 2024年第2期22卷 213-221页

作者： Yanxin Fu Wenxiao Zhao Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing100049China

We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.

关键词： ARX system Stochastic gradient algorithm Sparse identification support recovery Parameter estimation Strong consistency

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Improved RIP-based performance guarantees for multipath matching pursuit

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Science China(Information Sciences) 2018年第10期61卷 173-186页

作者： Juan ZHAO Xia BAI Ran TAO School of Information and Electronics Beijing Institute of Technology Beijing Key Laboratory of Fractional Signals and Systems Beijing Institute of Technology

The multipath matching pursuit(MMP) is a generalization of the orthogonal matching pursuit(OMP), which generates multiple child paths for every candidate in each iteration and selects the candidate having the minimal residual as the final support set when iteration ends. In this paper we analyze its performance in both noiseless and noisy cases. The restricted isometry property(RIP)-based condition of MMP that ensures accurate recovery of sparse signals in the noiseless case is derived by using a simple technique. The performance guarantees of the MMP for support recovery in noisy cases are also *** is shown that under certain conditions on the RIP and minimum magnitude of nonzero components of the sparse signal, the MMP will exactly recover the true support of the sparse signal in cases of bounded noises and recover the true support with a high probability in the case of Gaussian noise. Our bounds on the RIP improve the existing results.

关键词： compressed sensing(CS) sparse signal reconstruction multipath matching pursuit(MMP) support recovery restricted isometry property(RIP)

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