The DOI matches its Crossref record; 30 of the 30 references it cites were found in a registry or an index.
Sparse permutation invariant covariance estimation
Open accessAbstract
The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a lasso-type penalty. We establish a rate of convergence in the Frobenius norm as both data dimension p and sample size n are allowed to grow, and show that the rate depends explicitly on how sparse the true concentration matrix is. We also show that a correlation-based version of the method exhibits better rates in the operator norm. We also derive a fast iterative algorithm for computing the estimator, which relies on the popular Cholesky decomposition of the inverse but produces a permutation-invariant estimator. The method is compared to other estimators on simulated data and on a real data example of tumor tissue classification using gene expression data.
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Cites
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Fan, J., & Li, R. (2001) · Journal of the American Statistical Association · doi:10.1198/016214501753382273 · Cited by 8,900
Sparse inverse covariance estimation with the graphical lasso
Friedman, J., Hastie, T., & Tibshirani, R. (2008) · Biostatistics · doi:10.1093/biostatistics/kxm045 · Cited by 6,355
Alon, U., Barkai, N., Notterman, D. A., Gish, K., Ybarra, S., Mack, D., & Levine, A. J. (1999) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.96.12.6745 · Cited by 4,167
A well-conditioned estimator for large-dimensional covariance matrices
Ledoit, O., & Wolf, M. (2004) · Journal of Multivariate Analysis · doi:10.1016/s0047-259x(03)00096-4 · Cited by 3,046
High-dimensional graphs and variable selection with the Lasso
Meinshausen, N., & Bühlmann, P. (2006) · The Annals of Statistics · doi:10.1214/009053606000000281 · Cited by 2,521
Nonlinear Programming: Theory and Algorithms
Bazaraa, M. S., Sherali, H. D., & Shetty, C. M. (2006) · Wiley eBooks · doi:10.1002/0471787779 · Cited by 2,369
On the distribution of the largest eigenvalue in principal components analysis
Johnstone, I. M. (2001) · The Annals of Statistics · doi:10.1214/aos/1009210544 · Cited by 1,949
Pathwise coordinate optimization
Friedman, J., Hastie, T., Höfling, H., & Tibshirani, R. (2007) · The Annals of Applied Statistics · doi:10.1214/07-aoas131 · Cited by 1,895
Model selection and estimation in the Gaussian graphical model
Yuan, M., & Lin, Y. (2007) · Biometrika · doi:10.1093/biomet/asm018 · Cited by 1,627
Regularized estimation of large covariance matrices
Bickel, P. J., & Levina, E. (2008) · The Annals of Statistics · doi:10.1214/009053607000000758 · Cited by 934
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Self-citation
Metadata
- Authors
- Rothman, A. J., Bickel, P. J., Levina, E., & Zhu, J.
- Venue
- Electronic Journal of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2008-01-01
- Volume
- 2
- Issue
- none
- Pages
- 494-515
- ISSN
- 1935-7524 (ISSN-L)
- OpenAlex
- W1974105260
- Cited by
- 560
- References
- 30
- FWCI
- 16.14
- Type
- journal article
- Language
- en
- Open access
- gold
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
