Regularized group regression methods for genomic prediction: Bridge, MCP, SCAD, group bridge, group lasso, sparse group lasso, group MCP and group SCAD

BMC Proceedings

Volumn 8, Issue , 2014, Pages

  Ogutu, Joseph O ^a   Piepho, Hans Peter ^a  

^a UNIVERSITY OF HOHENHEIM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

MOLECULAR MARKER;

ACCURACY; BREEDING; BRIDGE REGRESSION; CHROMOSOME; CONFERENCE PAPER; GENETIC ASSOCIATION; GENETIC MARKER; GENETIC PROCEDURES; GENOME ANALYSIS; GENOMIC PREDICTION; GENOTYPE; GROUP BRIDGE REGRESSION; GROUP LASSO REGRESSION; GROUP MINIMAX CONCAVE PENALTY; GROUP SMOOTHLY CLIPPED ABSOLUTE DEVIATION; MINIMAX CONCAVE PENALTY; PERFORMANCE; PHENOTYPE; QUANTITATIVE TRAIT; QUANTITATIVE TRAIT LOCUS; REGRESSION ANALYSIS; SIMULATION; SINGLE NUCLEOTIDE POLYMORPHISM; SMOOTHLY CLIPPED ABSOLUTE DEVIATION; SPARSE GROUP LASSO REGRESSION; VALIDATION PROCESS;

EID: 85018193104     PISSN: None     EISSN: 17536561     Source Type: Journal    
DOI: 10.1186/1753-6561-8-S5-S7     Document Type: Conference Paper

References (41)

1. Meuwissen THE, Hayes BJ, Goddard ME: Prediction of total genetic value using genome-wide dense marker maps. Genetics. 2001, 157: 1819-1829.
2. Kennard RW: Ridge regression: biased estimation for non-orthogonal problems. Technometrics. 1970, 12: 55-67. 10.1080/00401706.1970.10488634.
3. Tibshirani R: Regression shrinkage and selection via the lasso. J Roy Statist Soc Ser B. 1996, 58: 267-288.
4. Hastie T: Regularization and variable selection via the elastic net. J Roy Statist Soc Ser B. 2005, 67: 301-320. 10.1111/j.1467-9868.2005.00503.x.
5. Frank IE, Friedman JH: A statistical view of some chemometrics regression tools (with discussion). Technometrics. 1993, 35: 109-148. 10.1080/00401706.1993.10485033.
6. Heslot N, Yang HP, Sorrells ME, Jannink JL: Genomic selection in plant breeding: a comparison of models. Crop Sci. 2012, 52: 146-160. 10.2135/cropsci2011.06.0297.
7. Ogutu JO, Schulz-Streeck T, Piepho H-P: Genomic selection using regularized linear regression models: ridge regression, lasso, elastic net and their extensions. BMC Proceedings. 2012, BioMed Central Ltd, 6 (Suppl 2)
8. Huang J, Horowitz JL, Ma S: Asymptotic properties of bridge estimators in sparse high-dimensional regression models. Ann Statist. 2008, 36: 587-613. 10.1214/009053607000000875.
9. Fu WJ: Penalized regressions: The bridge versus the lasso. J Comput Graph Statist. 1998, 7: 397-416.
10. Knight K, Fu W: Asymptotics for Lasso-type estimators. Ann Statist. 2000, 28: 356-1378.
11. Fan J, Li R: Variable selection via nonconcave penalized likelihood and its oracle Properties. J Amer Statist Assoc. 2001, 96: 1348-1360. 10.1198/016214501753382273.
12. Fan J, Peng H: Nonconcave penalized likelihood with a diverging number of parameters. Ann Stat. 2004, 32: 928-961. 10.1214/009053604000000256.
13. Whittaker JC, Thompson R, Denham MC: Marker-assisted selection using ridge regression. Genet Res. 2000, 75: 249-252. 10.1017/S0016672399004462.
14. Piepho HP: Ridge regression and extensions for genomewide selection in maize. Crop Sci. 2009, 49: 1165-1176. 10.2135/cropsci2008.10.0595.
15. Piepho H-P, Ogutu JO, Schulz-Streeck T, Estaghvirou B, Gordillo A, Technow F: Efficient computation of ridge-regression best linear unbiased prediction in genomic selection in plant breeding. Crop Sci. 2012, 52: 1093-1104. 10.2135/cropsci2011.11.0592.
16. Zhang CH: Nearly unbiased variable selection under minimax concave penalty. Ann Stat. 2010, 38: 894-942. 10.1214/09-AOS729.
17. Zhang CH: Penalized linear unbiased selection. 2007, Department of Statistics and Bioinformatics, Rutgers University, Technical Report #2007-003
18. Zhou H: The adaptive lasso and its oracle properties. J Amer Stat Assoc. 2006, 101: 1418-1429. 10.1198/016214506000000735.
19. Breheny P, Huang J: Penalized methods for bi-level variable selection. Stat Interface. 2009, 2: 369-380. 10.4310/SII.2009.v2.n3.a10.
20. Breheny P, Huang J: Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection. Ann Appl Stat. 2011, 5: 232-253. 10.1214/10-AOAS388.
21. Huang J, Breheny P, Ma S: A selective review of group selection in high-dimensional models. Statist Sci. 2012, 27: 481-499. 10.1214/12-STS392.
22. Huang J, Ma S, Xie H, Zhang CH: A group bridge approach for variable selection. Biometrika. 2009, 96: 339-355. 10.1093/biomet/asp020.
23. Park C, Yoon YJ: Bridge regression: adaptivity and group selection. J Statist Plann Inference. 2011, 141: 3506-3519. 10.1016/j.jspi.2011.05.004.
24. Yuan M, Lin Y: Model selection and estimation in regression with grouped variables. J Roy Statist Soc Ser B. 2006, 68: 49-67. 10.1111/j.1467-9868.2005.00532.x.
25. Simon N, Friedman J, Hastie T, Tibshirani R: A sparse-group lasso. J Comput Graph Statist. 2013, 22: 231-245. 10.1080/10618600.2012.681250.
26. Nardi Y, Rinaldo A: On the asymptotic properties of the group lasso estimator for linear models. Electron J Statist. 2008, 2: 605-633. 10.1214/08-EJS200.
27. Wang H, Leng C: A note on adaptive group lasso. Comput Statist Appl Data Anal. 2008, 52: 5277-5286. 10.1016/j.csda.2008.05.006.
28. Zhang C-H, Huang J: The sparsity and bias of the lasso selection in high-dimensional linear regression. Ann Stat. 2008, 36: 1567-1594. 10.1214/07-AOS520.
29. Peng J, Zhu J, Bergamaschi A, Han W, Noh DY, Pollack JR, Wang P: Regularized multivariate regression for identifying master predictors with application to integrative genomics study of breast cancer. Ann Appl Stat. 2010, 4: 53-77. 10.1214/09-AOAS271.
30. Friedman J, Hastie T, Tibshirani R: A note on the group lasso and sparse group lasso. 2010, arXiv preprint arXiv:1001.0736
31. Friedman J, Hastie T, Tibshirani R: Regularization paths for generalized linear models via coordinate descent. 2008, [ http://www-stat.stanford.edu/~hastie/Papers/glmnet.pdf ]
32. Yang Y: Can the strengths of AIC and BIC be shared?. Biometrika. 2005, 92: 937-950. 10.1093/biomet/92.4.937.
33. Martinez JG, Carroll RJ, Müller S, Sampson JN, Chartterjee N: Empirical performance of cross-validation with oracle methods in genomic context. Amer Statist. 2011, 65: 223-228. 10.1198/tas.2011.11052.
34. Jacob L, Obozinski G, Vert J-P: Group lasso with overlap and graph lasso. Proceedings of the 26th annual international conference on machine learning. Montreal, Canada. ICML 2009, 433-440. ACM, New York, NY, USA
35. Percival D: Theoretical properties of the overlapping groups lasso. Electron J Stat. 2011, 1-21.
36. Zhao P, Rocha G, Yu B: The composite absolute penalties family for grouped and hierarchical variable selection. Ann Stat. 2009, 37: 3468-3497. 10.1214/07-AOS584.
37. Bien J, Taylor J, Tibshirani R: A lasso for hierarchical interactions. Ann Stat. 2013, 41: 1111-1141. 10.1214/13-AOS1096. 2013
38. Lim M, Hastie T: Learning interactions through hierarchical group-lasso regularization. [ http://arxiv.org/pdf/1308.2719v1.pdf ]
39. Meier L, van der Geer S, Bühlmann P: The group lasso for logistic regression. J Roy Statist Soc Ser B. 2008, 70: 53-71. 10.1111/j.1467-9868.2007.00627.x.
40. Roth V, Fischer B: The group-lasso for generalized linear models: uniqueness of solutions and efficient algorithms. Proceedings of the 25th annual international conference on machine learning. 2009, Helsinski, Finland. ICML, 433-440.
41. Bach F: Consistency of the group lasso and multiple kernel learning. J Mach Learn. 2008, 9: 1179-1225.