The DOI matches its Crossref record; 92 of the 92 references it cites were found in a registry or an index.
Optimization with Sparsity-Inducing Penalties
Open accessAbstract
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate nonsmooth norms. The goal of this monograph is to present from a general perspective optimization tools and techniques dedicated to such sparsity-inducing penalties. We cover proximal methods, block-coordinate descent, reweighted l2-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provide an extensive set of experiments to compare various algorithms from a computational point of view.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
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
Greedy function approximation: A gradient boosting machine
Friedman, J. H. (2001) · The Annals of Statistics · doi:10.1214/aos/1013203451 · Cited by 30,731
Regularization and Variable Selection Via the Elastic Net
Zou, H., & Hastie, T. (2005) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2005.00503.x · Cited by 20,957
Boyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2011) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000016 · Cited by 17,075
(2021) · A First Course in Statistical Programming with R · doi:10.1017/9781108993456.011 · Cited by 13,724
Boyd, S. (2010) · now publishers, Inc. eBooks · doi:10.1561/9781601984616 · Cited by 12,677
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Beck, A., & Teboulle, M. (2009) · SIAM Journal on Imaging Sciences · doi:10.1137/080716542 · Cited by 11,952
Bertsekas, D. P. (1997) · Journal of the Operational Research Society · doi:10.1038/sj.jors.2600425 · Cited by 11,726
$rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
Aharon, M., Elad, M., & Bruckstein, A. (2006) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2006.881199 · Cited by 9,451
Cited by
Optimization Methods for Large-Scale Machine Learning
Bottou, L., Curtis, F. E., & Nocedal, J. (2018) · SIAM Review · doi:10.1137/16m1080173 · Cited by 3,128
Learning to learn by gradient descent by gradient descent
Andrychowicz, M., Denil, M., Gomez, S., Hoffman, M. W., Pfau, D., Schaul, T., Shillingford, B., & de Freitas, N. (2016) · arXiv · doi:10.48550/arxiv.1606.04474 · Cited by 1,486
FastText.zip: Compressing text classification models
Joulin, A., Grave, E., Bojanowski, P., Douze, M., Jégou, H., & Mikolov, T. (2016) · arXiv · doi:10.48550/arxiv.1612.03651 · Cited by 887
Group Sparse Beamforming for Green Cloud-RAN
(2014) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2014.040214.131770 · Cited by 468
Komodakis, N., & Pesquet, J.-C. (2015) · IEEE Signal Processing Magazine · doi:10.1109/msp.2014.2377273 · Cited by 419
Metadata
- Authors
- Bach, F., Jenatton, R., Mairal, J., & Obozinski, G.
- Venue
- Foundations and Trends® in Machine Learning
- Publisher
- Emerald
- Published
- 2025-12-17
- Volume
- 4
- Issue
- 1
- Pages
- 1-106
- ISSN
- 1935-8237 (ISSN-L)
- 1935-8245
- OpenAlex
- W2952139899
- Cited by
- 730
- References
- 92
- FWCI
- 58.13
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Optimization with Sparsity-Inducing Penalties. https://app.cochat.ai/papers/10.1561/2200000015
- The paper
- Bach, F., Jenatton, R., Mairal, J., & Obozinski, G. (2025). Optimization with Sparsity-Inducing Penalties. Foundations and Trends® in Machine Learning. https://doi.org/10.1561/2200000015
Data sources
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.
