101
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Parametric programming-based approximate selective inference for adaptive lasso, adaptive elastic net and group lasso

&
Received 10 Mar 2023, Accepted 24 Mar 2024, Published online: 09 Apr 2024

References

  • Ioannidis JP. Why most published research findings are false. Getting to Good: Research Integrity in the Biomedical Sciences. 2005; Vol. 2(8). p. 0696–0701.
  • Tibshirani R. Regression shrinkage and selection via the lasso. J R Stat Soc Ser B: Methodol. 1996;58(1):267–288.
  • Tibshirani R, Saunders M, Rosset S, et al. Sparsity and smoothness via the fused lasso. J R Stat Soc Ser B: Stat Methodol. 2005;67(1):91–108. doi: 10.1111/j.1467-9868.2005.00490.x
  • Zou H. The adaptive lasso and its oracle properties. J Am Stat Assoc. 2006;101(476):1418–1429. doi: 10.1198/016214506000000735
  • Zou H, Zhang HH. On the adaptive elastic-net with a diverging number of parameters. Ann Stat. 2009;37(4):1733–1751. doi: 10.1214/08-AOS625
  • Yuan M, Lin Y. Model selection and estimation in regression with grouped variables. J R Stat Soc Ser B: Stat Methodol. 2006;68(1):49–67. doi: 10.1111/j.1467-9868.2005.00532.x
  • Ma S, Song X, Huang J. Supervised group lasso with applications to microarray data analysis. BMC Bioinform. 2007;8(1):60–60. doi: 10.1186/1471-2105-8-60
  • Fithian W, Sun D, Taylor J. Optimal inference after model selection; 2014. doi: 10.48550/arXiv.1410.2597.
  • Taylor J, Tibshirani RJ. Statistical learning and selective inference. Proc Nati Acad Sci. 2015;112(25):7629–7634. doi: 10.1073/pnas.1507583112
  • Tibshirani RJ, Taylor J, Lockhart R, et al. Exact post-selection inference for sequential regression procedures. J Am Stat Assoc. 2016;111(514):600–620. doi: 10.1080/01621459.2015.1108848
  • Charkhi A, Claeskens G. Asymptotic post-selection inference for the Akaike information criterion. Biometrika. 2018;105(3):645–664. doi: 10.1093/biomet/asy018
  • Rügamer D, Greven S. Selective inference after likelihood- or test-based model selection in linear models. Stat Probab Lett. 2018;140:7–12. doi: 10.1016/j.spl.2018.04.010
  • Garcia-Angulo A, Claeskens G. Exact uniformly most powerful post-selection confidence distributions. Scand J Stat. 2023;50:358–382.
  • Hyun S, Lin KZ, G'Sell M, et al. Post-selection inference for changepoint detection algorithms with application to copy number variation data. Biometrics. 2021;77(3):1037–1049. doi: 10.1111/biom.v77.3
  • Berk R, Brown L, Buja A, et al. Valid post-selection inference. Ann Stat. 2013;41(2):802–837. doi: 10.1214/12-AOS1077
  • Taylor J, Tibshirani R. Post-selection inference for l1-penalized likelihood models. Can J Stat. 2018;46(1):41–61. doi: 10.1002/cjs.v46.1
  • Schultheiss C, Renaux C, Bühlmann P. Multicarving for high-dimensional post-selection inference. Electron J Stat. 2021;15(1):1695–1742. doi: 10.1214/21-EJS1825.
  • Garcia-Angulo A, Claeskens G. Optimal finite sample post-selection confidence distributions in generalized linear models. J Stat Plan Inference. 2023;222:66–77. doi: 10.1016/j.jspi.2022.06.001
  • Lee JD, Sun DL, Sun Y, et al. Exact post-selection inference, with application to the lasso. Ann Stat. 2016;44(3):907–927. doi: 10.1214/15-AOS1371
  • Liu K, Markovic J, Tibshirani R. More powerful post-selection inference, with application to the lasso; 2018. doi: 10.48550/arXiv.1801.09037.
  • Duy VNL, Takeuchi I. More powerful conditional selective inference for generalized lasso by parametric programming. J Mach Learn Res. 2022;23(300):1–37.
  • Duy VNL, Takeuchi I. Parametric programming approach for more powerful and general lasso selective inference; 2020. doi: 10.48550/arXiv.2004.09749.
  • Loftus JR, Taylor JE. Selective inference in regression models with groups of variables; 2015. doi: 10.48550/arXiv.1511.01478.
  • Yang F, Barber RF, Jain P, et al. Selective inference for group-sparse linear models; 2016. doi: 10.48550/arXiv.1607.08211.
  • Panigrahi S, MacDonald PW, Kessler D. Approximate post-selective inference for regression with the group lasso; 2020. doi: 10.48550/arXiv.2012.15664.
  • Tibshirani RJ, Taylor J. Degrees of freedom in lasso problems. Ann Stat. 2012;40(2):1198–1232. doi: 10.1214/12-AOS1003
  • Zou H, Hastie T. Regularization and variable selection via the elastic net. J R Stat Soc Ser B: Stat Methodol. 2005;67(2):301–320. doi: 10.1111/j.1467-9868.2005.00503.x
  • van de Geer S. Statistics for high-dimensional data: methods, theory and applications. 1st ed., Berlin, Heidelberg: Springer; 2011. (Springer Series in Statistics). Imprint: Springer.
  • Wang H, Leng C. A note on adaptive group lasso. Comput Stat Data Anal. 2008;52(12):5277–5286. doi: 10.1016/j.csda.2008.05.006
  • Wang M, Tian G. Adaptive group lasso for high-dimensional generalized linear models. Stat Papers. 2019;60:1469–1486. doi: 10.1007/s00362-017-0882-z
  • White H. Estimation, inference and specification analysis. Cambridge: Cambridge University Press; 1994.
  • Zhang Y, Li R, Tsai CL. Regularization parameter selections via generalized information criterion. J Am Stat Assoc. 2010;105(489):312–323. doi: 10.1198/jasa.2009.tm08013
  • Tsukurimichi T, Inatsu Y, Duy VNL. Conditional selective inference for robust regression and outlier detection using piecewise-linear homotopy continuation. Ann Inst Stat Math. 2022;74(6):1197–1228. doi: 10.1007/s10463-022-00846-2
  • R Core Team. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing; 2022.
  • Giesen J, Jaggi M, Laue S. Approximating parameterized convex optimization problems. ACM Trans Algorithms. 2012;9(1):1–17. doi: 10.1145/2390176.2390186
  • Ndiaye E, Le T, Fercoq O, et al. Safe grid search with optimal complexity. In: Proceedings of the 36th International Conference on Machine Learning. 2019; Vol. 97.
  • Kivaranovic D, Leeb H. On the length of post-model-selection confidence intervals conditional on polyhedral constraints. J Am Stat Assoc. 2021;116(534):845–857. doi: 10.1080/01621459.2020.1732989
  • Hosmer DW, Lemeshow S. Applied logistic regression. New York: Wiley; 1989. Wiley-interscience publications.
  • Scheetz TE, Kim KYA, Swiderski RE, et al. Regulation of gene expression in the mammalian eye and its relevance to eye disease. Proc Nati Acad Sci – PNAS. 2006;103(39):14429–14434. doi: 10.1073/pnas.0602562103
  • Yang Y, Zou H. A fast unified algorithm for solving group-lasso penalize learning problems. Stat Comput. 2015;25(6):1129–1141. doi: 10.1007/s11222-014-9498-5
  • Tian X, Taylor J. Selective inference with a randomized response. Ann Stat. 2018;46(2):679–710. doi: 10.1214/17-AOS1564
  • Min S, Zhou Q. Constructing confidence sets after lasso selection by randomized estimator augmentation; 2021. doi: 10.48550/arXiv.1904.08018.

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.