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We study sparse principal components analysis in the high-dimensional setting, where $p$ (the number of variables) can be much larger than $n$ (the number of observations).
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“Sparse principal component analysis”
Hui Zou, Trevor Hastie and Robert Tibshirani · 2006
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Alexandre d’Aspremont, Laurent El Ghaoui, Michael˜I. Jordan and Gert R.˜G. Lanckriet · 2007
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Y. Gordon, A.E. Litvak, S. Mendelson and A. Pajor · 2007
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“Concentration Inequalities and Model Selection”
Pascal Massart · 2007
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“Asymptotics of sample eigenstructure for a large dimensional spiked covariance model”
Debashis Paul · 2007
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“Augmented sparse principal component analysis for high dimensional Data” manuscript, 2007
Debashis Paul and Iain Johnstone · 2007
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“Covariance Regularization by Thresholding”
Peter˜J Bickel and Elizaveta Levina · 2008
“Finite sample approximation results for principal component analysis: A matrix perturbation approach”
Boaz Nadler · 2008
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“Sparse principal component analysis via regularized low rank matrix approximation”
Haipeng Shen and Jianhua˜Z. Huang · 2008
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“High-dimensional analysis of semidefinite relaxations for sparse principal components”
Arash˜A. Amini and Martin˜J. Wainwright · 2009
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“On consistency and sparsity for principal components analysis in high dimensions”
Iain˜M Johnstone and Arthur˜Yu Lu · 2009
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“Deflation methods for sparse PCA”
Lester Mackey · 2009
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“A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis”
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“Regularized estimation of large covariance matrices”
Peter˜J Bickel and Elizaveta Levina · 2008
Cited alongside, same era.
“Operator norm consistent estimation of large-dimensional sparse covariance matrices”
Noureddine El Karoui · 2008
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“Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning”
Alan˜J. Izenman · 2008
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Daniela˜M. Witten, Robert Tibshirani and Trevor Hastie · 2009
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“Optimal rates of convergence for covariance matrix estimation”
T˜Tony Cai, Cun-Hui Zhang and Harrison˜H Zhou · 2010
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“Empirical processes with a bounded ψ 1 \psi_{1} diameter”
Shahar Mendelson · 2010
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“Minimax rates of estimation for high-dimensional linear regression over ℓ q \ell_{q} -balls” to appear
Garvesh Raskutti, Martin˜J Wainwright and Bin Yu · 2011
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