Lasso regression under stochastic restrictions in linear regression: An application to genomic data

References

• Akaike, H. 1970. Statistical predictor identification. Annals of the Institute of Statistical Mathematics 22 (1):203–17. doi:10.1007/BF02506337.
   Web of Science ®Google Scholar
• Algamal, Z. Y., and M. H. Lee. 2015. Penalized logistic regression with the adaptive lasso for gene selection in high-dimensional cancer classification. Expert Systems with Applications 42 (23):9326–32. doi:10.1016/j.eswa.2015.08.016.
   Web of Science ®Google Scholar
• An, S., W. Liu, and S. Venkatesh. 2007. Face recognition using kernel ridge regression. In 2007 IEEE Conference on Computer Vision and Pattern Recognition, 1–7. IEEE. doi:10.1109/CVPR.2007.383105.
   Google Scholar
• Bielza, C., V. Robles, and P. Larrañaga. 2011. Regularized logistic regression without a penalty term: An application to cancer classification with microarray data. Expert Systems with Applications 38 (5):5110–8. doi:10.1016/j.eswa.2010.09.140.
   Web of Science ®Google Scholar
• Boyd, S., N. Parikh, E. Chu, B. Peleato, and J. Eckstein. 2011. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends® in Machine learning 3 (1):1–122.
   Google Scholar
• Bühlmann, P., M. Kalisch, and L. Meier. 2014. High-dimensional statistics with a view toward applications in biology. Annual Review of Statistics and Its Application 1 (1):255–78. doi:10.1146/annurev-statistics-022513-115545.
   Web of Science ®Google Scholar
• Butt, A. H., and Y. D. Khan. 2018. Prediction of s-sulfenylation sites using statistical moments based features via Chou’s 5-step rule. International Journal of Peptide Research and Therapeutics (IJPRT) 17:711–38.
   Google Scholar
• Chou, K. C. 2004. Review: Structural bioinformatics and its impact to biomedical science. Current Medicinal Chemistry 11 (16):2105–34. doi:10.2174/0929867043364667.
   PubMed Web of Science ®Google Scholar
• Chou, K. C. 2011. Some remarks on protein attribute prediction and pseudo amino acid composition. Journal of Theoretical Biology 273 (1):236–47. doi:10.1016/j.jtbi.2010.12.024.
   PubMed Web of Science ®Google Scholar
• Chou, K. C. 2015. Impacts of bioinformatics to medicinal chemistry. Medicinal Chemistry (Shariqah (United Arab Emirates)) 11 (3):218–34. doi:10.2174/1573406411666141229162834.
   PubMed Web of Science ®Google Scholar
• Chou, K. C. 2019a. Advances in predicting subcellular localization of multi-label proteins and its implication for developing multi-target drugs. Current Medicinal Chemistry 26 (26):4918–43. doi:10.2174/0929867326666190507082559.
   PubMed Web of Science ®Google Scholar
• Chou, K. C. 2019b. Impacts of pseudo amino acid components and 5-steps rule to proteomics and proteome analysis. Current Topics in Medicinal Chemistry 19 (25):2283–300. doi:10.2174/1568026619666191018100141.
   PubMed Web of Science ®Google Scholar
• Chou, K. C. 2020a. The development of Gordon life science institute: Its driving force and accomplishments. Natural Science 12 (4):202–17. doi:10.4236/ns.2020.124018.
   Google Scholar
• Chou, K. C. 2020b. Gordon life science institute and its impacts on computational biology and drug development. Natural Science 12 (3):125–61. doi:10.4236/ns.2020.123013.
   Google Scholar
• Chou, K. C. 2020c. Other mountain stones can attack jade: The 5-steps rule. Natural Science 12 (9):633–7. doi:10.4236/ns.2020.129048.
   Google Scholar
• Chou, K. C. 2020d. Proposing 5-steps rule is a notable milestone for studying molecular biology. Natural Science 12 (3):74–9. doi:10.4236/ns.2020.123011.
   Google Scholar
• Chou, K. C. 2020e. Using similarity software to evaluate scientific paper quality is a big mistake. Natural Science 12 (3):42–58. doi:10.4236/ns.2020.123008.
   Google Scholar
• Donoho, D. L., and J. M. Johnstone. 1994. Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 (3):425–55. doi:10.1093/biomet/81.3.425.
   Web of Science ®Google Scholar
• Du, X., Y. Diao, H. Liu, and S. Li. 2019. Msdbp: Exploring dna-binding proteins by integrating multiscale sequence information via Chou’s five-step rule. Journal of Proteome Research 18 (8):3119–32. doi:10.1021/acs.jproteome.9b00226.
   PubMed Web of Science ®Google Scholar
• Du, D., K. Li, X. Li, and M. Fei. 2014. A novel forward gene selection algorithm for microarray data. Neurocomputing 133:446–58. doi:10.1016/j.neucom.2013.12.012.
   Web of Science ®Google Scholar
• Efron, B., T. Hastie, I. Johnstone, and R. Tibshirani. 2004. Least angle regression. The Annals of Statistics 32 (2):407–99. doi:10.1214/009053604000000067.
   Web of Science ®Google Scholar
• Forrester, J., and J. Kalivas. 2004. Ridge regression optimization using a harmonious approach. Journal of Chemometrics 18 (7–8):372–84. doi:10.1002/cem.883.
   Web of Science ®Google Scholar
• Frank, L. E., and J. H. Friedman. 1993. A statistical view of some chemometrics regression tools. Technometrics 35 (2):109–35. doi:10.1080/00401706.1993.10485033.
   Web of Science ®Google Scholar
• Friedman, J., T. Hastie, H. Höfling, and R. Tibshirani. 2007. Pathwise coordinate optimization. The Annals of Applied Statistics 1 (2):302–32. doi:10.1214/07-AOAS131.
   Web of Science ®Google Scholar
• Friedman, J., T. Hastie, and R. Tibshirani. 2010. Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software 33 (1):1–22. doi:10.18637/jss.v033.i01.
   PubMed Web of Science ®Google Scholar
• Fu, W. J. 1998. Penalized regressions: The bridge versus the lasso. Journal of Computational and Graphical Statistics 7 (3):397–416.
   Web of Science ®Google Scholar
• Guler, H., and E. O. Guler. 2021a. Mixed lasso estimator for stochastic restricted regression models. Journal of Applied Statistics 48 (13–15):2795–808. doi:10.1080/02664763.2021.1922614.
   PubMed Web of Science ®Google Scholar
• Guler, H., and E. O. Guler. 2021b. Sparsely restricted penalized estimators. Communications in Statistics - Theory and Methods 50 (7):1656–70. doi:10.1080/03610926.2019.1682164.
   Web of Science ®Google Scholar
• Hastie, T., R. Tibshirani, and J. Friedman. 2009. The elements of statistical learning: Data mining, inference and prediction. 2nd ed. New York, NY: Springer.
   Google Scholar
• Hoerl, A. E., and R. W. Kennard. 1970. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics 12 (1):55–67. doi:10.1080/00401706.1970.10488634.
   Web of Science ®Google Scholar
• Hurvich, C. M., and C. L. Tsai. 1989. Regression and time series model selection in small samples. Biometrika 76 (2):297–307. doi:10.1093/biomet/76.2.297.
   Web of Science ®Google Scholar
• Javanmard, A., and A. Montanari. 2014. Confidence intervals and hypothesis testing for high-dimensional regression. The Journal of Machine Learning Research 15 (1):2869–909.
   Google Scholar
• Ju, Z., and S. Y. Wang. 2020. Prediction of lysine formylation sites using the composition of k-spaced amino acid pairs via Chou’s 5-steps rule and general pseudo components. Genomics 112 (1):859–66. doi:10.1016/j.ygeno.2019.05.027.
   PubMed Web of Science ®Google Scholar
• Kabir, M., S. Ahmad, M. Iqbal, and M. Hayat. 2020. inr-2l: A two-level sequence-based predictor developed via Chou’s 5-steps rule and general pseaac for identifying nuclear receptors and their families. Genomics 112 (1):276–85. doi:10.1016/j.ygeno.2019.02.006.
   PubMed Web of Science ®Google Scholar
• Kayanan, M., and P. Wijekoon. 2020. Stochastic restricted lasso-type estimator in the linear regression model. Journal of Probability and Statistics 2020:1–7. doi:10.1155/2020/7352097.
   Web of Science ®Google Scholar
• Kohannim, O., D. P. Hibar, J. L. Stein, N. Jahanshad, X. Hua, P. Rajagopalan, A. Toga, C. R. Jack, Jr, M. W. Weiner, G. I. De Zubicaray, et al. 2012. Discovery and replication of gene influences on brain structure using lasso regression. Frontiers in Neuroscience 6:115.
   PubMed Web of Science ®Google Scholar
• Li, W., J. Feng, and T. Jiang. 2011. Isolasso: A lasso regression approach to rna-seq based transcriptome assembly. Journal of Computational Biology : A Journal of Computational Molecular Cell Biology 18 (11):1693–707. doi:10.1089/cmb.2011.0171.
   PubMed Web of Science ®Google Scholar
• Manning, C., P. Raghavan, and H. Schütze. 2010. Introduction to information retrieval. Natural Language Engineering 16 (1):100–3.
   Google Scholar
• Osborne, M. R., B. Presnell, and B. A. Turlach. 2000. On the lasso and its dual. Journal of Computational and Graphical Statistics 9 (2):319–37.
   Web of Science ®Google Scholar
• Park, C., and Y. J. Yoon. 2011. Bridge regression: Adaptivity and group selection. Journal of Statistical Planning and Inference 141 (11):3506–19. doi:10.1016/j.jspi.2011.05.004.
   Web of Science ®Google Scholar
• Schwarz, G. 1978. Estimating the dimension of a model. The Annals of Statistics 6 (2):461–4. doi:10.1214/aos/1176344136.
   Web of Science ®Google Scholar
• Shao, Y. T., and K. C. Chou. 2020. ploc_deep-mvirus: A cnn model for predicting subcellular localization of virus proteins by deep learning. Natural Science 12 (6):388–99. doi:10.4236/ns.2020.126033.
   Google Scholar
• Shao, Y. T., X. X. Liu, Z. Lu, and K. C. Chou. 2020a. ploc_deep-mhum: Predict subcellular localization of human proteins by deep learning. Natural Science 12 (7):526–51. doi:10.4236/ns.2020.127042.
   Google Scholar
• Shao, Y. T., X. X. Liu, Z. Lu, and K. C. Chou. 2020b. ploc_deep-mplant: Predict subcellular localization of plant proteins by deep learning. Natural Science 12 (5):237–47. doi:10.4236/ns.2020.125021.
   Google Scholar
• Stamey, T. A., J. N. Kabalin, J. E. McNeal, I. M. Johnstone, F. Freiha, E. A. Redwine, and N. Yang. 1989. Prostate specific antigen in the diagnosis and treatment of adenocarcinoma of the prostate. ii. radical prostatectomy treated patients. Journal of Urology 141 (5):1076–83. doi:10.1016/S0022-5347(17)41175-X.
   PubMed Web of Science ®Google Scholar
• Tan, C. F., L. Wahidin, S. Khalil, N. Tamaldin, J. Hu, and G. Rauterberg. 2016. The application of expert system: A review of research and applications. ARPN Journal of Engineering and Applied Sciences 11 (4):2448–53.
   Google Scholar
• Theil, H., and A. S. Goldberger. 1961. On pure and mixed statistical estimation in economics. International Economic Review 2 (1):65–78. doi:10.2307/2525589.
   Web of Science ®Google Scholar
• Tibshirani, R. 1996. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological) 58 (1):267–88. doi:10.1111/j.2517-6161.1996.tb02080.x.
   Web of Science ®Google Scholar
• Tibshirani, R. 2011. Regression shrinkage and selection via the lasso: A retrospective. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73 (3):273–82. doi:10.1111/j.1467-9868.2011.00771.x.
   Web of Science ®Google Scholar
• Tibshirani, R., J. Bien, J. Friedman, T. Hastie, N. Simon, J. Taylor, and R. J. Tibshirani. 2012. Strong rules for discarding predictors in lasso-type problems. Journal of the Royal Statistical Society. Series B, Statistical Methodology 74 (2):245–66. doi:10.1111/j.1467-9868.2011.01004.x.
   PubMed Web of Science ®Google Scholar
• Wang, Y., Y. Jiang, J. Zhang, Z. Chen, B. Xie, and C. Zhao. 2022. Robust variable selection based on the random quantile LASSO. Communications in Statistics-Simulation and Computation 51 (1):29–39.
   Google Scholar
• Zhang, C., Y. Wu, and M. Zhu. 2019. Pruning variable selection ensembles. Statistical Analysis and Data Mining: The ASA Data Science Journal 12 (3):168–84. doi:10.1002/sam.11410.
   Web of Science ®Google Scholar
• Zheng, S., and W. Liu. 2011. An experimental comparison of gene selection by lasso and dantzig selector for cancer classification. Computers in Biology and Medicine 41 (11):1033–40. doi:10.1016/j.compbiomed.2011.08.011.
   PubMed Web of Science ®Google Scholar
• Zou, Y., Y. Ding, J. Tang, F. Guo, and L. Peng. 2019. Fkrr-mvsf: A fuzzy kernel ridge regression model for identifying dna-binding proteins by multi-view sequence features via chou’s five-step rule. International Journal of Molecular Sciences 20 (17):4175. doi:10.3390/ijms20174175.
   PubMed Web of Science ®Google Scholar