×

An overview of reciprocal \(L_1\)-regularization for high dimensional regression data. (English) Zbl 07910802


MSC:

62-08 Computational methods for problems pertaining to statistics
Full Text: DOI

References:

[1] TibshiraniR. Regression shrinkage and selection via the lasso. J R Stat Soc Ser B1996, 58:267-288. · Zbl 0850.62538
[2] ZhaoP, YuB. On model selection consistency of lasso. J Mach Learn Res2006, 7:2541-2563. · Zbl 1222.62008
[3] ZouH. The adaptive lasso and its oracle properties. J Am Stat Assoc2006, 101:1418-1429. · Zbl 1171.62326
[4] FanJ, LiR. Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc2001, 96:1348-1360. · Zbl 1073.62547
[5] ZhangC‐H. Nearly unbiased variable selection under minimax concave penalty. Ann Stat2010, 38:894-942. · Zbl 1183.62120
[6] ShenX, PanW, ZhuY. Likelihood‐based selection and sharp parameter estimation. J Am Stat Assoc2012, 107:223-232. · Zbl 1261.62020
[7] AkaikeH. A new look at statistical model identification. IEEE Trans Autom Control1974, 19:716-723. · Zbl 0314.62039
[8] SchwarzGE. Estimating the dimension of a model. Ann Stat1978, 6:461-464. · Zbl 0379.62005
[9] ChenJ, ChenZ. Extended bayesian information criteria for model selection with large model spaces. Biometrika2008, 95:759-771. · Zbl 1437.62415
[10] ChenJ, ChenZ. Extended BIC for small‐n‐large‐p sparse GLM. Stat Sin2012, 22:555-574. · Zbl 1238.62080
[11] LiangF. Some connections between bayesian and non‐bayesian methods for regression model selections. Stat Prob Lett2002, 57:53-63. · Zbl 0996.62020
[12] LiangF, ChengY, LinG. Simulated stochastic approximation annealing for global optimization with a square‐root cooling schedule. J Am Stat Assoc2014, 109:847-863. · Zbl 1367.62244
[13] ParkT, CasellaG. The Bayesian Lasso. J Am Stat Assoc2008, 103:681-686. · Zbl 1330.62292
[14] SongQ, LiangF. High‐dimensional variable selection with reciprocal l_1‐regularization. J Am Stat Assoc2015, 110:1607-1620. · Zbl 1373.62358
[15] WangL, ZhouW, HoetingJ. Identification of pairwise informative features for clustering data. Unpublished manuscript, 2016.
[16] JohnsonVE, RosselD. Bayesian model selection in high‐dimensional settings. J Am Stat Assoc2012, 107:649-660. · Zbl 1261.62024
[17] ShinM, BhattacharyaA, JohnsonVE. Scalable bayesian variable selection using nonlocal prior densities in ultrahigh‐dimensional settings. arXiv preprint arXiv:1507.07106, 2015.
[18] SongQ, LiangF. A split‐and‐merge Bayesian variable selection approach for ultra‐high dimensional regression. J R Stat Soc Ser B2015, 77:947-972. · Zbl 1414.62322
[19] NarisettyNN, HeX. Bayesian variable selection with shrinking and diffusing priors. Ann Stat2014, 42:789-817. · Zbl 1302.62158
[20] ZhangC‐H, HuangJ. The sparsity and bias of the lasso selection in high‐dimensional regression. Ann Stat2008, 36:1567-1594. · Zbl 1142.62044
[21] DavidsonK, SzarekS. Local operator theory, random matrics and banach spaces. In: JohnsonWB (ed.), LindenstraussJ (ed.), eds. Handbook on the Geometry of Banach Spaces. Amsterdam: North‐Holland; 2001, 317-366. · Zbl 1067.46008
[22] VershyninR. Introduction to the Non‐Asymptotic Analysis of Random Matrices. Cambridge: Cambridge Univ. Press; 2012, 210-268.
[23] MeinshausenN, YuB. Lasso‐type recovery of sparse representations for high‐dimensional data. Ann Stat2009, 39:246-270. · Zbl 1155.62050
[24] YangY, WainwrightMJ, JordanMI. On the computational complexity of high‐dimensional bayesian variable selection. Ann Stat2016, 44:2497-2532. · Zbl 1359.62088
[25] ZouH, LiR. One‐step sparse estimates in nonconcave penalized likelihood models. Ann Stat2008, 36:1509-1533. · Zbl 1142.62027
[26] EfronB, HastieT, JohnstonI, TibshiraniR. Least angle regression. Ann Stat2004, 32:407-499. · Zbl 1091.62054
[27] BrehenyP, HuangJ. Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection. Ann Appl Stat2011, 5:232-243. · Zbl 1220.62095
[28] FriedmanJ, HastieT, TibshiraniR. Regularization paths for generalized linear models via coordinate descent. J Stat Softw2010, 33:1-22.
[29] ZhuY. An augmented admm algorithm with application to the generalized lasso‐type recovery of sparse representations for high‐dimensional data problem. J Comput Graph Stat2017, 26:195-204.
[30] KirkpatrickS. Optimization by simulated annealing: quantitative studies. J Stat Phys1984, 34:975-986.
[31] HansC, DobraA, WestM. Shotgun stochastic search for large p regression. J Am Stat Assoc2007, 102:507-516. · Zbl 1134.62398
[32] LiangF, LiuC, CarrollRJ. Stochastic approximation in Monte Carlo computation. J Am Stat Assoc2007, 102:305-320. · Zbl 1226.65002
[33] LiangF, SongQ, YuK. Bayesian subset modeling for high dimensional generalized linear models. J Am Stat Assoc2013, 108:589-606. · Zbl 06195963
[34] HaarioH, SaksmanE. Simulated annealing process in general state space. Adv Appl Prob1991, 23:866-893. · Zbl 0744.60104
[35] ReidS, TibshiraniR, FriedmanJ. A study of error variance estimation in lasso regression. arXiv preprint arXiv:1311.5274, 2014.
[36] FanJ, LvJ. Sure independence screening for ultrahigh dimensional feature space. J R Stat Soc Ser B2008, 70:849-911. · Zbl 1411.62187
[37] FanJ, SongR. Sure independence screening in generalized linear model with np‐dimensionality. Ann Stat2010, 38:3567-3604. · Zbl 1206.68157
[38] FengY, YuY. Consistent cross‐validation for tuning parameter selection in high‐dimensional variable selection. arXiv preprint arXiv:1308.5390, 2013.
[39] ShaoJ. Linear model selection by cross‐validation. J Am Stat Assoc1993, 88:486-494. · Zbl 0773.62051
[40] YuY, YangF. Modified cross‐validation for penalized high‐dimensional linear regression models. J Comput Graph Stat2014, 23:1009-1027.
[41] ZhangY, YangY. Cross‐validation for selecting a model selection procedure. J Economet2015, 187:95-112. · Zbl 1337.62387
[42] LaurentB, MassartP. Adaptive estimation of a quadratic functional by model selection. Ann Stat2000, 28:1302-1338. · Zbl 1105.62328
[43] FoygelR, DrtonM. Bayesian model choice and information criteria in sparse generalized linear models. arXiv preprint arXiv:1112.5635, 2011.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.