The DOI matches its Crossref record; 16 of the 16 references it cites were found in a registry or an index.
The benefit of group sparsity
Open accessAbstract
This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is consistent with the data. Moreover, the theory predicts some limitations of the group Lasso formulation that are confirmed by simulation studies.
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Cites
Model Selection and Estimation in Regression with Grouped Variables
Yuan, M., & Lin, Y. (2006) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2005.00532.x · Cited by 7,261
Decoding by Linear Programming
Candes, E. J., & Tao, T. (2005) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.858979 · Cited by 7,121
Simultaneous analysis of Lasso and Dantzig selector
Bickel, P. J., Ritov, Y., & Tsybakov, A. B. (2009) · The Annals of Statistics · doi:10.1214/08-aos620 · Cited by 2,396
The Volume of Convex Bodies and Banach Space Geometry
Pisier, G. (1989) · Cambridge University Press eBooks · doi:10.1017/cbo9780511662454 · Cited by 967
An Empirical Bayesian Strategy for Solving the Simultaneous Sparse Approximation Problem
Wipf, D. P., & Rao, B. D. (2007) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2007.894265 · Cited by 911
Consistency of the group Lasso and multiple kernel learning
Bach, F. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0707.3390 · Cited by 669
Compressed Sensing and Redundant Dictionaries
Rauhut, H., Schnass, K., & Vandergheynst, P. (2008) · IEEE Transactions on Information Theory · doi:10.1109/tit.2008.920190 · Cited by 541
The sparsity and bias of the Lasso selection in high-dimensional linear regression
Zhang, C.-H., & Huang, J. (2008) · The Annals of Statistics · doi:10.1214/07-aos520 · Cited by 506
Self-citationJi, S., Dunson, D., & Carin, L. (2009) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2008.2005866 · Cited by 502
Support union recovery in high-dimensional multivariate regression
Obozinski, G., Wainwright, M. J., & Jordan, M. I. (2011) · The Annals of Statistics · doi:10.1214/09-aos776 · Cited by 350
Cited by
Block-Sparse Signals: Uncertainty Relations and Efficient Recovery
Eldar, Y. C., Kuppinger, P., & Bolcskei, H. (2010) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2010.2044837 · Cited by 1,313
Optimization with Sparsity-Inducing Penalties
Bach, F., Jenatton, R., Mairal, J., & Obozinski, G. (2025) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000015 · Cited by 730
Optimization with Sparsity-Inducing Penalties
Bach, F. (2011) · now publishers, Inc. eBooks · doi:10.1561/9781601985118 · Cited by 608
Estimation of (near) low-rank matrices with noise and high-dimensional scaling
Negahban, S., & Wainwright, M. J. (2011) · The Annals of Statistics · doi:10.1214/10-aos850 · Cited by 537
Structured Variable Selection with Sparsity-Inducing Norms
Jenatton, R., Audibert, J.-Y., & Bach, F. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0904.3523 · Cited by 431
Metadata
- Authors
- Huang, J., & Zhang, T.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2010-08-01
- Volume
- 38
- Issue
- 4
- Pages
- 1978-2004
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2077964948
- Cited by
- 521
- References
- 16
- FWCI
- 32.59
- Type
- journal article
- Language
- en
- Open access
- bronze
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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.
