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We study optimal estimation for sparse principal component analysis when the number of non-zero elements is small but on the same order as the dimension of the data.
J. Yedidia, W. Freeman, and Y. Weiss, “Understanding belief propagation and its generalizations,” in Exploring Artificial Intelligence in the New Millennium . San Francisco, USA: Morgan Kaufmann, 2003, pp. 239–236
2003
Earlier work this paper cites.
D. C. Hoyle and M. Rattray, “Principal-component-analysis eigenvalue spectra from data with symmetry-breaking structure,” Physical Review E , vol. 69, no. 2, p. 026124, 2004
2004
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B. Moghaddam, Y. Weiss, and S. Avidan, “Spectral bounds for sparse pca: Exact and greedy algorithms,” in Advances in neural information processing systems , 2005, pp. 915–922
2005
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J. Baik, G. Ben Arous, and S. Péché, “Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices,” Annals of Probability , pp. 1643–1697, 2005
2005
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H. Zou, T. Hastie, and R. Tibshirani, “Sparse principal component analysis,” Journal of computational and graphical statistics , vol. 15, no. 2, pp. 265–286, 2006
2006
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A. d’Aspremont, F. Bach, and L. E. Ghaoui, “Optimal solutions for sparse principal component analysis,” The Journal of Machine Learning Research , vol. 9, pp. 1269–1294, 2008
2008
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I. M. Johnstone and A. Y. Lu, “On consistency and sparsity for principal components analysis in high dimensions,” Journal of the American Statistical Association , vol. 104, no. 486, 2009
2009
Cited alongside, same era.
A. A. Amini and M. J. Wainwright, “High-dimensional analysis of semidefinite relaxations for sparse principal components,” Annals of statistics , vol. 37, no. 5, pp. 2877–2921, 2009
2009
Cited alongside, same era.
S. Rangan and A. K. Fletcher, “Iterative estimation of constrained rank-one matrices in noise,” in Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on . IEEE, 2012, pp. 1246–1250
2012
Cited alongside, same era.
2013
Cited alongside, same era.
R. Matsushita and T. Tanaka, “Low-rank matrix reconstruction and clustering via approximate message passing,” in Advances in Neural Information Processing Systems , 2013, pp. 917–925
2013
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2013
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D. L. Donoho, A. Javanmard, and A. Montanari, “Information-theoretically optimal compressed sensing via spatial coupling and approximate message passing,” IEEE transactions on information theory , vol. 59, no. 11, pp. 7434–7464, 2013
2013
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Y. Deshpande and A. Montanari, “Information-theoretically optimal sparse pca,” in Information Theory (ISIT), 2014 IEEE International Symposium on , 2014, pp. 2197–2201
2014
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2013
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2014
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