Previous Articles Next Articles
Didi Lv^{1}, Xiaoqun Zhang^{2}
Didi Lv, Xiaoqun Zhang. A GREEDY ALGORITHM FOR SPARSE PRECISION MATRIX APPROXIMATION[J]. Journal of Computational Mathematics, 2021, 39(5): 693707.
[1] A. Beck and M. Teboulle, A fast iterative shrinkagethresholding algorithm for linear inverse problems, SIAM Journal on Imaging Sciences, 2:1(2009), 183202, [2] P. J. Bickel, E. Levina, et al., Covariance regularization by thresholding, The Annals of Statistics, 36:6(2008), 25772604. [3] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. [4] M. Burger, G. Gilboa, S. Osher, J. Xu, et al., Nonlinear inverse scale space methods, Communications in Mathematical Sciences, 4:1(2006), 179212. [5] M. Burger, M. Möller, M. Benning, and S. Osher, An adaptive inverse scale space method for compressed sensing, Mathematics of Computation, 82:281(2013), 269299. [6] J.F. Cai, S. Osher, and Z. Shen, Convergence of the linearized bregman iteration for l1norm minimization, Mathematics of Computation, 78:268(2008), 21272136. [7] J.F. Cai, S. Osher, and Z. Shen, Linearized bregman iterations for compressed sensing, Mathematics of Computation, 78:267(2009), 15151536. [8] T.T. Cai, W. Liu, and X. Luo, A Constrained l_{1} Minimization Approach to Sparse Precision Matrix Estimation, Journal of the American Statistical Association, 106:494(2011), 594607. [9] T.T. Cai, W. Liu, and H.H. Zhou, Estimating Sparse Precision Matrix:Optimal Rates of Convergence and Adaptive Estimation, Annals of Statistics, 44:2(2016), 455488. [10] E. Candes and J. Romberg, l_{1}magic:Recovery of sparse signals via convex programming, URL:www.acm.caltech.edu/l1magic/downloads/l1magic.pdf, 4:14(2005). [11] T.F.C. Chan and R. Glowinski, Finite element approximation and iterative solution of a class of mildly nonlinear elliptic equations, Computer Science Department, Stanford University Stanford, 1978. [12] A. d'Aspremont, O. Banerjee, and L. El Ghaoui, Firstorder methods for sparse covariance selection, SIAM Journal on Matrix Analysis and Applications, 30:1(2008), 5666. [13] E. Esser, Applications of lagrangianbased alternating direction methods and connections to split bregman, CAM report, 9(2009), 31. [14] J. Fan, Y. Feng, and Y. Wu, Network exploration via the adaptive lasso and scad penalties, The Annals of Applied Statistics, 3:2(2009), 521. [15] J. Fan and R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, Journal of the American Statistical Association, 96:456(2001), 13481360. [16] S. Foucart, Hard thresholding pursuit:An algorithm for compressive sensing, SIAM Journal on Numerical Analysis, 49:6(2011), 25432563. [17] F. Simon, Stability and robustness of weak orthogonal matching pursuits, Recent Advances in Harmonic Analysis and Applications, Springer, (2012), 395405. [18] J. Friedman, T. Hastie, and R. Tibshirani, Sparse inverse covariance estimation with the graphical lasso, Biostatistics, 9:3(2008), 432441. [19] D. Gabay and B. Mercier, A dual algorithm for the solution of non linear variational problems via finite element approximation, Institut de recherche d'informatique et d'automatique, 1975. [20] E.T. Hale, W. Yin, and Y. Zhang, Fixedpoint continuation for l_{1}minimization:Methodology and convergence, SIAM Journal on Optimization, 19:3(2008), 11071130. [21] C. Lam and J. Fan, Sparsistency and rates of convergence in large covariance matrix estimation, Annals of Statistics, 37:6B (2009), 4254. [22] W. Liu and X. Luo, Fast and adaptive sparse precision matrix estimation in high dimensions, Journal of Multivariate Analysis, 135(2015), 153162. [23] S. Mallat and Z. Zhang, Matching pursuit with timefrequency dictionaries, Courant Institute of Mathematical Sciences, New York, Unit, Tech. Rep., 1993. [24] M. Möller and Xiaoqun Zhang, Fast sparse reconstruction:Greedy inverse scale space flows, Mathematics of Computation, 85(2016), 179208. [25] D. Needell and J. A. Tropp, Cosamp:Iterative signal recovery from incomplete and inaccurate samples, Applied and Computational Harmonic Analysis, 26:3(2009), 301321. [26] S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, An iterative regularization method for total variationbased image restoration, Multiscale Modeling & Simulation, 4:2(2005), 460489. [27] S. Osher, Y. Mao, B. Dong, and W. Yin, Fast linearized bregman iteration for compressive sensing and sparse denoising, arXiv preprint arXiv:1104.0262, 2011. [28] Y.C. Pati, R. Rezaiifar, and P.S. Krishnaprasad, Orthogonal matching pursuit:Recursive function approximation with applications to wavelet decomposition, IEEE Proceedings of 27th Asilomar Conference on Signals, Systems and Computers, (1993), 4044. [29] P. Ravikumar, M.J. Wainwright, G. Raskutti, B. Yu et al., Highdimensional covariance estimation by minimizing l_{1}penalized logdeterminant divergence, Electronic Journal of Statistics, 5(2011), 935980. [30] A.J. Rothman, P.J. Bickel, E. Levina, and J. Zhu, Sparse permutation invariant covariance estimation, Electronic Journal of Statistics, 2:3(2008), 494515. [31] J.A. Tropp, Greed is good:Algorithmic results for sparse approximation, IEEE Transactions on Information Theory, 50:10(2004), 22312242. [32] J.A. Tropp and A.C. Gilbert, Signal recovery from random measurements via orthogonal matching pursuit, IEEE Transactions on Information Theory, 53:12(2007), 46554666. [33] W.B. Wu and M. Pourahmadi, Nonparametric estimation of large covariance matrices of longitudinal data, Biometrika, 90:4(2003), 831844. [34] W. Yin, S. Osher, D. Goldfarb, and J. Darbon, Bregman iterative algorithms for l_{1}minimization with applications to compressed sensing, SIAM Journal on Imaging Sciences, 1:1(2008), 143168. [35] M. Yuan, High dimensional inverse covariance matrix estimation via linear programming, Journal of Machine Learning Research, 11:Aug (2010), 22612286. [36] M. Yuan and Y. Lin, Model selection and estimation in the gaussian graphical model, Biometrika, 94:1(2007), 1935. [37] X. Zhang, M. Burger, and S. Osher, A unified primaldual algorithm framework based on bregman iteration, Journal of Scientific Computing, 46:1(2011), 2046. [38] H. Zou, The adaptive lasso and its oracle properties, Journal of the American Statistical Association, 101:476(2006), 14181429. 
[1]  Yijun Zhong, Chongjun Li. PIECEWISE SPARSE RECOVERY VIA PIECEWISE INVERSE SCALE SPACE ALGORITHM WITH DELETION RULE [J]. Journal of Computational Mathematics, 2020, 38(2): 375394. 
Viewed  
Full text 


Abstract 

