244
Views
1
CrossRef citations to date
0
Altmetric
Dimension Reduction and Sparse Modeling

On Exact Feature Screening in Ultrahigh-Dimensional Binary Classification

ORCID Icon, ORCID Icon, ORCID Icon & ORCID Icon
Pages 448-462 | Received 23 Jul 2022, Accepted 26 Sep 2023, Published online: 27 Nov 2023

References

  • Balakrishnan, N., and Stepanov, A. (2008), “Asymptotic Properties of the Ratio of Order Statistics,” Statistics & Probability Letters, 78, 301–310. DOI: 10.1016/j.spl.2007.08.001.
  • Balasubramanian, K., Sriperumbudur, B., and Lebanon, G. (2013), “Ultrahigh Dimensional Feature Screening via RKHS Embeddings,” in Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics (Vol. 31), eds. C. M. Carvalho and P. Ravikumar, pp. 126–134, Scottsdale, Arizona, USA, PMLR.
  • Baringhaus, L., and Franz, C. (2010), “Rigid Motion Invariant Two-Sample Tests,” Statistica Sinica, 20, 1333–1361.
  • Bien, J., Taylor, J., and Tibshirani, R. (2013), “A LASSO for Hierarchical Interactions,” The Annals of Statistics, 41, 1111–1141. DOI: 10.1214/13-AOS1096.
  • Bittner, M., Meltzer, P., Chen, Y., Jiang, Y., Seftor, E., Hendrix, M., Radmacher, M., Simon, R., Yakhini, Z., Ben-Dor, A., Sampas, N., Dougherty, E., Wang, E., Marincola, F., Gooden, C., Lueders, J., Glatfelter, A., Pollock, P., Carpten, J., Gillanders, E., Leja, D., Dietrich, K., Beaudry, C., Berens, M., Alberts, D., and Sondak, V. (2000), “Molecular Classification of Cutaneous Malignant Melanoma by Gene Expression Profiling,” Nature, 406, 536–540. DOI: 10.1038/35020115.
  • Cheng, G., Li, X., Lai, P., Song, F., and Yu, J. (2017), “Robust Rank Screening for Ultrahigh Dimensional Discriminant Analysis,” Statistics and Computing, 27, 535–545. DOI: 10.1007/s11222-016-9637-2.
  • Cui, H., Li, R., and Zhong, W. (2015), “Model-Free Feature Screening for Ultrahigh Dimensional Discriminant Analysis,” Journal of the American Statistical Association, 110, 630–641. DOI: 10.1080/01621459.2014.920256.
  • Deegalla, S., and Bostrom, H. (2006), “Reducing High-Dimensional Data by Principal Component Analysis vs. Random Projection for Nearest Neighbor Classification,” in 2006 5th International Conference on Machine Learning and Applications (ICMLA’06), pp. 245–250.
  • Derigs, U. (1988), “Solving Non-bipartite Matching Problems via Shortest Path Techniques,” Annals of Operations Research, 13, 225–261. DOI: 10.1007/BF02288324.
  • Dutta, S., and Genton, M. G. (2014), “A Non-gaussian Multivariate Distribution with all Lower-Dimensional Gaussians and Related Families,” Journal of Multivariate Analysis, 132, 82–93. DOI: 10.1016/j.jmva.2014.07.007.
  • Fan, J., and Fan, Y. (2008), “High Dimensional Classification Using Features Annealed Independence Rules,” The Annals of Statistics, 36, 2605–2637. DOI: 10.1214/07-AOS504.
  • Fan, J., and Lv, J. (2008), “Sure Independence Screening for Ultrahigh Dimensional Feature Space,” Journal of the Royal Statistical Society, Series B, 70, 849–911. DOI: 10.1111/j.1467-9868.2008.00674.x.
  • Fan, J., and Song, R. (2010), “Sure Independence Screening in Generalized Linear Models with NP-Dimensionality,” The Annals of Statistics, 38, 3567–3604. DOI: 10.1214/10-AOS798.
  • Feller, W. (1971), An Introduction to Probability Theory and its Applications (Vol. II, 2nd ed.), New York-London-Sydney: Wiley.
  • Gretton, A., Bousquet, O., Smola, A., and Schölkopf, B. (2005), “Measuring Statistical Dependence with Hilbert-Schmidt Norms,” in Algorithmic Learning Theory: 16th International Conference, ALT 2005, Singapore, October 8-11, 2005. Proceedings 16, pp. 63–77, Springer.
  • Guyon, I., Gunn, S., Ben-Hur, A., and Dror, G. (2005), “Result Analysis of the NIPS 2003 Feature Selection Challenge,” in Advances in Neural Information Processing Systems, eds. L. Saul, Y. Weiss, and L. Bottou, Cambridge, MA: MIT Press.
  • Hao, N., Feng, Y., and Zhang, H. H. (2018), “Model Selection for High-Dimensional Quadratic Regression via Regularization,” Journal of the American Statistical Association, 113, 615–625. DOI: 10.1080/01621459.2016.1264956.
  • Hao, N., and Zhang, H. H. (2014), “Interaction Screening for Ultrahigh-Dimensional Data,” Journal of the American Statistical Association, 109, 1285–1301. DOI: 10.1080/01621459.2014.881741.
  • Hastie, T., Tibshirani, R., and Friedman, J. (2009), The Elements of Statistical Learning: Data mining, Inference, and Prediction, New York: Springer.
  • He, S., Ma, S., and Xu, W. (2019), “A Modified Mean-Variance Feature-Screening Procedure for Ultrahigh-Dimensional Discriminant Analysis,” Computational Statistics & Data Analysis, 137, 155–169. DOI: 10.1016/j.csda.2019.02.003.
  • Jiang, H., Zhao, X., Ma, R. C. W., and Fan, X. (2022), “Consistent Screening Procedures in High-Dimensional Binary Classification,” Statistica Sinica, 32, 109–130. DOI: 10.5705/ss.202020.0088.
  • John, G. H., Kohavi, R., and Pfleger, K. (1994), “Irrelevant Features and the Subset Selection Problem,” in Machine Learning Proceedings 1994, pp. 121–129, Elsevier.
  • Li, Y., Hong, H. G., and Li, Y. (2019), “Multiclass Linear Discriminant Analysis with Ultrahigh-Dimensional Features,” Biometrics, 75, 1086–1097. DOI: 10.1111/biom.13065.
  • Lu, B., Greevy, R., Xu, X., and Beck, C. (2011), “Optimal Nonbipartite Matching and its Statistical Applications,” The American Statistician, 65, 21–30. DOI: 10.1198/tast.2011.08294.
  • Mai, Q., and Zou, H. (2013), “The Kolmogorov Filter for Variable Screening in High-Dimensional Binary Classification,” Biometrika, 100, 229–234. DOI: 10.1093/biomet/ass062.
  • Meier, L., Van De Geer, S., and Bühlmann, P. (2008), “The Group Lasso for Logistic Regression,” Journal of the Royal Statistical Society, Series B, 70, 53–71. DOI: 10.1111/j.1467-9868.2007.00627.x.
  • Nelder, J. A. (1977), “A Reformulation of Linear Models,” Journal of the Royal Statistical Society, Series A, 140, 48–77. DOI: 10.2307/2344517.
  • Ni, L., and Fang, F. (2016), “Entropy-based Model-Free Feature Screening for Ultrahigh-Dimensional Multiclass Classification,” Journal of Nonparametric Statistics, 28, 515–530. DOI: 10.1080/10485252.2016.1167206.
  • Pan, R., Wang, H., and Li, R. (2016), “Ultrahigh-Dimensional Multiclass Linear Discriminant Analysis by Pairwise Sure Independence Screening,” Journal of the American Statistical Association, 111, 169–179. DOI: 10.1080/01621459.2014.998760.
  • Pfister, N., Bühlmann, P., Schölkopf, B., and Peters, J. (2018), “Kernel-based Tests for Joint Independence,” Journal of the Royal Statistical Society, Series B, 80, 5–31. DOI: 10.1111/rssb.12235.
  • Roy, S., Sarkar, S., Dutta, S., and Ghosh, A. K. (2022), “On Generalizations of Some Distance based Classifiers for HDLSS Data,” Journal of Machine Learning Research, 23, 1–41.
  • Shen, C., Panda, S., and Vogelstein, J. T. (2022), “The Chi-square Test of Distance Correlation,” Journal of Computational and Graphical Statistics, 31, 254–262. DOI: 10.1080/10618600.2021.1938585.
  • Sheng, Y., and Wang, Q. (2020), “Model-Free Feature Screening for Ultrahigh Dimensional Classification,” Journal of Multivariate Analysis, 178, 104618. DOI: 10.1016/j.jmva.2020.104618.
  • Shipp, M. A., Ross, K. N., Tamayo, P., Weng, A. P., Kutok, J. L., Aguiar, R. C., Gaasenbeek, M., Angelo, M., Reich, M., Pinkus, G. S., et al. (2002), “Diffuse Large b-Cell Lymphoma Outcome Prediction by Gene-Expression Profiling and Supervised Machine Learning,” Nature Medicine, 8, 68–74. DOI: 10.1038/nm0102-68.
  • Simon, N., Friedman, J., Hastie, T., and Tibshirani, R. (2013), “A Sparse-Group Lasso,” Journal of Computational and Graphical Statistics, 22, 231–245. DOI: 10.1080/10618600.2012.681250.
  • Song, F., Lai, P., Shen, B., and Cheng, G. (2018), “Variance Ratio Screening for Ultrahigh Dimensional Discriminant Analysis,” Communications in Statistics. Theory and Methods, 47, 6034–6051. DOI: 10.1080/03610926.2017.1406113.
  • Song, L., Smola, A., Gretton, A., Bedo, J., and Borgwardt, K. (2012), “Feature Selection via Dependence Maximization,” Journal of Machine Learning Research, 13, 1393–1434.
  • Székely, G. J., and Rizzo, M. L. (2004), “Testing for Equal Distributions in High Dimension,” InterStat, 5, 1249–1272.
  • ——- (2005), “A New Test for Multivariate Normality,” Journal of Multivariate Analysis, 93, 58–80.
  • Székely, G. J., Rizzo, M. L., and Bakirov, N. K. (2007), “Measuring and Testing Dependence by Correlation of Distances,” The Annals of Statistics, 35, 2769–2794. DOI: 10.1214/009053607000000505.
  • Wang, Z., Deng, G., and Xu, H. (2023), “Group Feature Screening based on Gini Impurity for Ultrahigh-Dimensional Multi-Classification,” AIMS Mathematics, 8, 4342–4362. DOI: 10.3934/math.2023216.
  • Yi, C., and Huang, J. (2017), “Semismooth Newton Coordinate Descent Algorithm for Elastic-Net Penalized Huber Loss Regression and Quantile Regression,” Journal of Computational and Graphical Statistics, 26, 547–557. DOI: 10.1080/10618600.2016.1256816.
  • Zhu, L.-P., Li, L., Li, R., and Zhu, L.-X. (2011), “Model-Free Feature Screening for Ultrahigh-Dimensional Data,” Journal of the American Statistical Association, 106, 1464–1475. DOI: 10.1198/jasa.2011.tm10563.

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.