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First-Order Methods for Sparse Covariance Selection
Open accessAbstract
Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample data and to highlight conditional independence relationships between the sample variables. We first formulate a convex relaxation of this combinatorial problem, we then detail two efficient first-order algorithms with low memory requirements to solve large-scale, dense problem instances.
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Citations
Cites
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
Cited by
Regularized estimation of large covariance matrices
Bickel, P. J., & Levina, E. (2008) · The Annals of Statistics · doi:10.1214/009053607000000758 · Cited by 934
Covariance regularization by thresholding
Bickel, P. J., & Levina, E. (2008) · The Annals of Statistics · doi:10.1214/08-aos600 · Cited by 893
High-dimensional covariance estimation by minimizing ℓ1-penalized log-determinant divergence
Ravikumar, P., Wainwright, M. J., Raskutti, G., & Yu, B. (2011) · Electronic Journal of Statistics · doi:10.1214/11-ejs631 · Cited by 744
Phase recovery, MaxCut and complex semidefinite programming
Waldspurger, I., d’Aspremont, A., & Mallat, S. (2015) · Mathematical Programming · doi:10.1007/s10107-013-0738-9 · Cited by 573
Self-citationSparse permutation invariant covariance estimation
Rothman, A. J., Bickel, P. J., Levina, E., & Zhu, J. (2008) · Electronic Journal of Statistics · doi:10.1214/08-ejs176 · Cited by 560
Metadata
- Authors
- d'Aspremont, A., Banerjee, O., & El Ghaoui, L.
- Venue
- SIAM Journal on Matrix Analysis and Applications
- Published
- 2008-01
- Volume
- 30
- Issue
- 1
- Pages
- 56-66
- ISSN
- 0895-4798 (ISSN-L)
- 1095-7162
- OpenAlex
- W2044600950
- Cited by
- 343
- References
- 2
- FWCI
- 23.59
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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