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High-dimensional generalized linear models and the lasso
Open accessAbstract
We consider high-dimensional generalized linear models with Lipschitz loss functions, and prove a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty. The penalty is based on the coefficients in the linear predictor, after normalization with the empirical norm. The examples include logistic regression, density estimation and classification with hinge loss. Least squares regression is also discussed.
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Cites
The Elements of Statistical Learning
Hastie, T., Friedman, J., & Tibshirani, R. (2001) · Springer Series in Statistics · doi:10.1007/978-0-387-21606-5 · Cited by 24,162
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Belloni, A., Chernozhukov, V., & Hansen, C. (2014) · Journal of Economic Perspectives · doi:10.1257/jep.28.2.29 · Cited by 722
Cross-Validation With Confidence
Lei, J. (2020) · Journal of the American Statistical Association · doi:10.1080/01621459.2019.1672556 · Cited by 93
Double/debiased machine learning for difference-in-differences models
Chang, N.-C. (2020) · The Econometrics Journal · doi:10.1093/ectj/utaa001 · Cited by 93
Guo, W., & Lin, S. (2009) · Genetic Epidemiology · doi:10.1002/gepi.20382 · Cited by 51
Fair Regression with Wasserstein Barycenters
Chzhen, E., Denis, C., Hebiri, M., Oneto, L., & Pontil, M. (2020) · arXiv · doi:10.48550/arxiv.2006.07286 · Cited by 46
“We refer to [3, 15, 29, 30, 39] for various examples of estimators and additional assumptions such that the bound in Assumption 4.3 is satisfied.”
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Metadata
- Authors
- van de Geer, S. A.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2008-04-01
- Volume
- 36
- Issue
- 2
- Pages
- 614-645
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2142246398
- Cited by
- 414
- References
- 1
- FWCI
- 20.49
- Type
- journal article
- Language
- en
- Open access
- bronze
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