2,301
Views
18
CrossRef citations to date
0
Altmetric
Theory and Methods

Robust Variable and Interaction Selection for Logistic Regression and General Index Models

&
Pages 271-286 | Received 01 Feb 2017, Published online: 28 Jun 2018

References

  • Anderson, T. W. (1958), An Introduction to Multivariate Statistical Analysis, New York: Wiley.
  • Beer, D. G., Kardia, S. L., Huang, C.-C., Giordano, T. J., Levin, A. M., Misek, D. E., Lin, L., Chen, G., Gharib, T. G., Thomas, D. G., Lizyness, M. L., Kuick, R., Hayasaka, S., Taylor, J. M. G., Iannettoni, M. D., Orringer, M. B., and Hanash, S. (2002), “Gene-Expression Profiles Predict Survival of Patients With Lung Adenocarcinoma,” Nature Medicine, 8, 816–824.
  • Bien, J., Taylor, J., and Tibshirani, R. (2013), “A Lasso for Hierarchical Interactions,” The Annals of Statistics, 41, 1111–1141.
  • Boser, B. E., Guyon, I. M., and Vapnik, V. N. (1992), “A Training Algorithm for Optimal Margin Classifiers,” in Proceedings of the Fifth Annual Workshop on Computational Learning Theory, ACM, pp. 144–152.
  • Breiman, L. (2001), “Random Forests,” Machine Learning, 45, 5–32.
  • Broman, K. W., and Speed, T. P. (2002), “A Model Selection Approach for the Identification of Quantitative Trait Loci in Experimental Crosses,” Journal of the Royal Statistical Society, Series B, 64, 641–656.
  • Cai, T., and Liu, W. (2011), “A Direct Estimation Approach to Sparse Linear Discriminant Analysis,” Journal of the American Statistical Association, 106, 1566–1577.
  • Chen, J., and Chen, Z. (2008), “Extended Bayesian Information Criteria for Model Selection With Large Model Spaces,” Biometrika, 95, 759–771.
  • ——— (2012), “Extended BIC for Small-n-Large-P Sparse GLM,” Statistica Sinica, 22, 555–574.
  • Chowdhary, R., Zhang, J., and Liu, J. S. (2009), “Bayesian Inference of Protein–Protein Interactions From Biological Literature,” Bioinformatics, 25, 1536–1542.
  • Clemmensen, L., Hastie, T., Witten, D., and Ersbøll, B. (2011), “Sparse Discriminant Analysis,” Technometrics, 53, 406–413.
  • Cook, R. D. (2007), “Fisher Lecture: Dimension Reduction in Regression,” Statistical Science, 22, 1–26.
  • Efron, B. (2009), “Empirical Bayes Estimates for Large-Scale Prediction Problems,” Journal of the American Statistical Association, 104, 1015–1028.
  • ——— (2010), Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction (Vol. 1), Cambridge: Cambridge University Press.
  • Fan, J., and Fan, Y. (2008), “High Dimensional Classification Using Features Annealed Independence Rules,” Annals of Statistics, 36, 2605–2637.
  • Fan, Y., Jin, J., and Yao, Z. (2013), “Optimal Classification in Sparse Gaussian Graphic Model,” The Annals of Statistics, 41, 2537–2571.
  • Fan, Y., Kong, Y., Li, D., and Zheng, Z. (2015), “Innovated Interaction Screening for High-Dimensional Nonlinear Classification,” The Annals of Statistics, 43, 1243–1272.
  • Foygel, R., and Drton, M. (2011), “Bayesian Model Choice and Information Criteria in Sparse Generalized Linear Models,” arXiv preprint arXiv:1112.5635.
  • Guo, Y., Hastie, T., and Tibshirani, R. (2007), “Regularized Linear Discriminant Analysis and Its Application in Microarrays,” Biostatistics, 8, 86–100.
  • Han, F., Zhao, T., and Liu, H. (2013), “Coda: High Dimensional Copula Discriminant Analysis,” The Journal of Machine Learning Research, 14, 629–671.
  • Jia, J., and Yu, B. (2010), “On Model Selection Consistency of the Elastic Net When p≫n,” Statistica Sinica, 20, 595–611.
  • Jiang, B., and Liu, J. S. (2014), “Variable Selection for General Index Models via Sliced Inverse Regression,” The Annals of Statistics, 42, 1751–1786.
  • Joachims, T. (1998), Text Categorization With Support Vector Machines: Learning With Many Relevant Features, New York: Springer.
  • Li, K.-C. (1991), “Sliced Inverse Regression for Dimension Reduction,” Journal of the American Statistical Association, 86, 316–327.
  • Li, L. (2007), “Sparse Sufficient Dimension Reduction,” Biometrika, 94, 603–613.
  • Li, L., Dennis Cook, R., and Nachtsheim, C. J. (2005), “Model-Free Variable Selection,” Journal of the Royal Statistical Society, Series B, 67, 285–299.
  • Li, R., Zhong, W., and Zhu, L. (2012), “Feature Screening via Distance Correlation Learning,” Journal of the American Statistical Association, 107, 1129–1139.
  • Lin, Q., Zhao, Z., and Liu, J. S. (2018a), “On Consistency and Sparsity for Sliced Inverse Regression in High Dimensions,” Annals of Statistics, 46, 580–610.
  • ——— (2018b), “Sparse Sliced Inverse Regression for High Dimensional Data,” Journal of the American Statistical Association, under revision.
  • Mai, Q., Zou, H., and Yuan, M. (2012), “A Direct Approach to Sparse Discriminant Analysis in Ultra-High Dimensions,” Biometrika, 99, 29–42.
  • Maugis, C., Celeux, G., and Martin-Magniette, M.-L. (2011), “Variable Selection in Model-Based Discriminant Analysis,” Journal of Multivariate Analysis, 102, 1374–1387.
  • Murphy, T. B., Dean, N., and Raftery, A. E. (2010), “Variable Selection and Updating in Model-Based Discriminant Analysis for High Dimensional Data With Food Authenticity Applications,” The Annals of Applied Statistics, 4, 396–421.
  • Phillips, P. J. (1998), Support Vector Machines Applied to Face Recognition (Vol. 285), Gaithersburg, MD: NIST.
  • Ravikumar, P., Wainwright, M. J., and Lafferty, J. D. (2010), “High-Dimensional Ising Model Selection Using l1-Regularized Logistic Regression,” The Annals of Statistics, 38, 1287–1319.
  • Schwarz, G. (1978), “Estimating the Dimension of a Model,” The Annals of Statistics, 6, 461–464.
  • Shao, J., Wang, Y., Deng, X., and Wang, S. (2011), “Sparse Linear Discriminant Analysis by Thresholding for High Dimensional Data,” The Annals of Statistics, 39, 1241–1265.
  • Simon, N., and Tibshirani, R. (2016), “A Permutation Approach to Testing Interactions in Many Dimensions,” Journal of the American Statistical Association, 110, 1707–1716.
  • Singh, D., Febbo, P. G., Ross, K., Jackson, D. G., Manola, J., Ladd, C., Tamayo, P., Renshaw, A. A., D’Amico, A. V., Richie, J. P., Lander, E. S., Loda, M., Kantoff, P. W., Golub, T. R., and Sellers, W. R. (2002), “Gene Expression Correlates of Clinical Prostate Cancer Behavior,” Cancer Cell, 1, 203–209.
  • Szretter, M. E., and Yohai, V. J. (2009), “The Sliced Inverse Regression Algorithm as a Maximum Likelihood Procedure,” Journal of Statistical Planning and Inference, 139, 3570–3578.
  • Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288.
  • Tibshirani, R., Hastie, T., Narasimhan, B., and Chu, G. (2002), “Diagnosis of Multiple Cancer Types by Shrunken Centroids of Gene Expression,” Proceedings of the National Academy of Sciences, 99, 6567–6572.
  • Vershynin, R. (2012), “Introduction to the Non-Asymptotic Analysis of Random Matrices,” in Compressed Sensing: Theory and Applications, eds. Y. Eldar and G. Kutyniok, Cambridge: Cambridge University Press, pp. 210–268.
  • Waldmann, P., Mészáros, G., Gredler, B., Fuerst, C., and Sölkner, J. (2013), “Evaluation of the Lasso and the Elastic Net in Genome-Wide Association Studies,” Frontiers in Genetics, 4, 270.
  • Wang, H. (2009), “Forward Regression for Ultra-High Dimensional Variable Screening,” Journal of the American Statistical Association, 104, 1512–1524.
  • Wasserman, L., and Roeder, K. (2009), “High Dimensional Variable Selection,” Annals of Statistics, 37, 2178–2201.
  • Witten, D. M., and Tibshirani, R. (2011), “Penalized Classification Using Fisher’s Linear Discriminant,” Journal of the Royal Statistical Society, Series B, 73, 753–772.
  • Yu, Y., and Feng, Y. (2014), “Modified Cross-Validation for Penalized High-Dimensional Linear Regression Models,” Journal of Computational and Graphical Statistics, 23, 1009–1027.
  • Zhang, Q., and Wang, H. (2011), “On BIC’s Selection Consistency for Discriminant Analysis,” Statistica Sinica, 21, 731–740.
  • Zhao, P., and Yu, B. (2006), “On Model Selection Consistency of Lasso,” The Journal of Machine Learning Research, 7, 2541–2563.
  • Zhong, W., Zhang, T., Zhu, Y., and Liu, J. S. (2012), “Correlation Pursuit: Forward Stepwise Variable Selection for Index Models,” Journal of the Royal Statistical Society, Series B, 74, 849–870.
  • 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.

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.