1,714
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

A Pliable Lasso

&
Pages 215-225 | Received 26 Dec 2017, Accepted 03 Jul 2019, Published online: 05 Sep 2019

References

  • Athey, S., Tibshirani, J., and Wager, S. (2019), “Generalized Random Forests,” The Annals of Statistics, 47, 1148–1178, DOI:10.1214/18-AOS1709.
  • Bach, F., Jenatton, R., Mairal, J., and Obozinski, G. (2012), “Structured Sparsity Through Convex Optimization,” Statistical Science, 27, 450–468, DOI:10.1214/12-STS394.
  • Bien, J., Taylor, J., and Tibshirani, R. (2013), “A Lasso for Hierarchical Interactions,” The Annals of Statistics, 42, 1111–1141. DOI:10.1214/13-AOS1096.
  • Chen, X., Lin, Q., and Sen, B. (2019), “On Degrees of Freedom of Projection Estimators With Applications to Multivariate Nonparametric Regression,” Journal of the American Statistical Association, 1–30. DOI:10.1080/01621459.2018.1537917.
  • Cleveland, W., Grosse, E., Shyu, W., and Terpenning, I. (1991), “Local Regression Models,” in Statistical Models in S, eds. J. Chambers and T. Hastie, Pacific Grove, CA: Wadsworth & Brooks.
  • Du, W., and Tibshirani, R. (2018), “A Pliable Lasso for the Cox Model,” arXiv no. 1807.06770.
  • Eberlin, L. S., Tibshirani, R. J., Zhang, J., Longacre, T. A., Berry, G. J., Bingham, D. B., Norton, J. A., Zare, R. N., and Poultsides, G. A. (2014), “Molecular Assessment of Surgical-Resection Margins of Gastric Cancer by Mass-Spectrometric Imaging,” Proceedings of the National Academy of Sciences of the United States of America, 111, 2436–2441. DOI:10.1073/pnas.1400274111.
  • Efron, B. (1986), “How Biased Is the Apparent Error Rate of a Prediction Rule?,” Journal of the American Statistical Association, 81, 461–70. DOI:10.1080/01621459.1986.10478291.
  • Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2004), “Least Angle Regression” (with discussion, and a rejoinder by the authors), The Annals of Statistics, 32, 407–499. DOI:10.1214/009053604000000067.
  • El Ghaoui, L., Viallon, V., and Rabbani, T. (2010), “Safe Feature Elimination in Sparse Supervised Learning,” Pacific Journal of Optimization, 6, 667–698.
  • Friedman, J., Hastie, T., and Tibshirani, R. (2010), “Regularization Paths for Generalized Linear Models via Coordinate Descent,” Journal of Statistical Software, 33, 1–22. DOI:10.18637/jss.v033.i01.
  • Haris, A., Witten, D., and Simon, N. (2016), “Convex Modeling of Interactions With Strong Heredity,” Journal of Computational and Graphical Statistics, 25, 981–1004, DOI:10.1080/10618600.2015.1067217.
  • Hastie, T., and Tibshirani, R. (1993), “Varying Coefficient Models” (with discussion), Journal of the Royal Statistical Society, Series B, 55, 757–796. DOI:10.1111/j.2517-6161.1993.tb01939.x.
  • Kato, K. (2009), “On the Degrees of Freedom in Shrinkage Estimation,” Journal of Multivariate Analysis, 100, 1338–1352. DOI:10.1016/j.jmva.2008.12.002.
  • Lim, M., and Hastie, T. (2014), “Learning Interactions via Hierarchical Group-Lasso Regularization,” Journal of Computational and Graphical Statistics, 24, pp. 627–654. DOI:10.1080/10618600.2014.938812.
  • Ndiaye, E., Fercoq, O., Gramfort, A., and Salmon, J. (2016), “Gap Safe Screening Rules for Sparse-Group Lasso,” in Advances in Neural Information Processing Systems (Vol. 29), eds. D. D. Lee, M. Sugiyama, U. V. Luxburg, I. Guyon, and R. Garnett, Red Hook, NY: Curran Associates, Inc., pp. 388–396.
  • Pashova, H., LeBlanc, M., and Kooperberg, C. (2017), “Structured Detection of Interactions With the Directed Lasso,” Statistics in Biosciences, 9, 676–691, DOI:10.1007/s12561-016-9184-6.
  • Powers, S., Hastie, T., and Tibshirani, R. (2015), “Customized Training With an Application to Mass Spectrometric Imaging of Cancer Tissue,” The Annals of Applied Statistics, 9, 1709–1725. DOI:10.1214/15-AOAS866.
  • Powers, S., Qian, J., Jung, K., Schuler, A., Shah, N. H., Hastie, T., and Tibshirani, R. (2018), “Some Methods for Heterogeneous Treatment Effect Estimation in High-Dimensions,” Statistics in Medicine, 37, 1767–1787. DOI:10.1002/sim.7623.
  • R Core Team (2019), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing, available at https://www.R-project.org/.
  • Rhee, S.-Y., Gonzales, M. J., Kantor, R., Betts, B. J., Ravela, J., and Shafer, R. W. (2003), “Human Immunodeficiency Virus Reverse Transcriptase and Protease Sequence Database,” Nucleic Acids Research, 31, 298–303. DOI:10.1093/nar/gkg100.
  • Rothenhäusler, D., Meinshausen, N., Bühlmann, P., and Peters, J. (2018), “Anchor Regression: Heterogeneous Data Meets Causality,” arXiv no. 1801.06229.
  • She, Y., Wang, Z., and Jiang, H. (2016), “Group Regularized Estimation Under Structural Hierarchy,” Journal of the American Statistical Association, 113, 445–454, DOI:10.1080/01621459.2016.1260470.
  • Simon, N., Friedman, J., Hastie, T., and Tibshirani, R. (2013), “A Sparse-Group Lasso,” Journal of Computational and Graphical Statistics, 22, 231–245. DOI:10.1080/10618600.2012.681250.
  • Tibshirani, R., Bien, J., Friedman, J. Hastie, T., Simon, N. Taylor, J. and Tibshirani, R. (2012), “Strong Rules for Discarding Predictors in Lasso-Type Problems,” Journal of the Royal Statistical Society, Series B, 74, 245–266. DOI:10.1111/j.1467-9868.2011.01004.x.
  • Tibshirani, R. J., and Taylor, J. (2012), “Degrees of Freedom in Lasso Problems,” Annals of Statistics, 40, 1198–1232. DOI:10.1214/12-AOS1003.
  • Wager, S., and Athey, S. (2018), “Estimation and Inference of Heterogeneous Treatment Effects Using Random Forests,” Journal of the American Statistical Association, 113, 1228–1242, DOI:10.1080/01621459.2017.1319839.
  • Wang, J., Lin, B., Gong, P., Wonka, P., and Ye, J. (2013), Lasso Screening Rules via Dual Polytope Projection,” in Advances in Neural Information Processing Systems (NIPS Conference Proceedings), pp. 1070–1078.
  • Yan, X., and Bien, J. (2017), “Hierarchical Sparse Modeling: A Choice of Two Group Lasso Formulations,” Statistical Science, 32, 531–560, DOI:10.1214/17-STS622.
  • Yuan, M., and Lin, Y. (2007), “Model Selection and Estimation in Regression With Grouped Variables,” Journal of the Royal Statistical Society, Series B, 68, 49–67. DOI:10.1111/j.1467-9868.2005.00532.x.
  • Zhao, P., Rocha, G., and Yu, B. (2009), “The Composite Absolute Penalties Family for Grouped and Hierarchical Variable Selection,” The Annals of Statistics, 37, 3468–3497. DOI:10.1214/07-AOS584.
  • Zou, H., and Hastie, T. (2005), ‘Regularization and Variable Selection via the Elastic Net,” Journal of the Royal Statistical Society, Series B, 67, 301–320. DOI:10.1111/j.1467-9868.2005.00503.x.
  • Zou, H., Hastie, T., and Tibshirani, R. (2007), “On the Degrees of Freedom of the Lasso,” The Annals of Statistics, 35, 2173–2192. DOI:10.1214/009053607000000127.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.