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Minimax bounds for sparse PCA with noisy high-dimensional data
Open accessAbstract
We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish a lower bound on the minimax risk of estimators under the $l_{2}$ loss, in the joint limit as dimension and sample size increase to infinity, under various models of sparsity for the population eigenvectors. The lower bound on the risk points to the existence of different regimes of sparsity of the eigenvectors. We also propose a new method for estimating the eigenvectors by a two-stage coordinate selection scheme.
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Citations
Cites
Sparse Principal Component Analysis
Zou, H., Hastie, T., & Tibshirani, R. (2006) · Journal of Computational and Graphical Statistics · doi:10.1198/106186006x113430 · Cited by 3,152
Cited by
Principal component analysis: A review and recent developments
Jolliffe, I. T., & Cadima, J. (2016) · Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rsta.2015.0202 · Cited by 10,117
Large Covariance Estimation by Thresholding Principal Orthogonal Complements
Fan, J., Liao, Y., & Mincheva, M. (2013) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/rssb.12016 · Cited by 909
Robust covariance and scatter matrix estimation under Huber’s contamination model
Chen, M., Gao, C., & Ren, Z. (2018) · The Annals of Statistics · doi:10.1214/17-aos1607 · Cited by 146
Sparse principal component analysis for high-dimensional stationary time series
Fujimori, K., Goto, Y., Liu, Y., & Taniguchi, M. (2023) · Scandinavian Journal of Statistics · doi:10.1111/sjos.12664 · Cited by 7
Metadata
- Authors
- Birnbaum, A., Johnstone, I. M., Nadler, B., & Paul, D.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2013-06-01
- Volume
- 41
- Issue
- 3
- Pages
- 1055-1084
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W1994938797
- Cited by
- 180
- References
- 1
- FWCI
- 17.20
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Birnbaum, A., Johnstone, I. M., Nadler, B., & Paul, D. (2013). Minimax bounds for sparse PCA with noisy high-dimensional data. The Annals of Statistics. https://doi.org/10.1214/12-aos1014
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