Discriminant analysis on high dimensional Gaussian copula model. (English) Zbl 1398.62164
Summary: In this paper we propose a classifier for the high dimensional Gaussian copula model. Besides, a Rotate-and-Solve procedure is proposed to tackle with the non-sparse case. Both theoretical analysis and simulation study show that the classifier performs better than some state-of-the-art methods.
MSC:
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 62H12 | Estimation in multivariate analysis |
References:
| [1] | Anderson, T. W., An Introduction to Multivariate Statistical Analysis (2003), Wiley-Interscience · Zbl 0083.14601 |
| [2] | Anderson, T. W.; Fang, K. T., Theory and applications of elliptically contoured and related distributions. Technical Report (1990), DTIC Document · Zbl 0747.00016 |
| [3] | Bickel, P. J.; Levina, E., Some theory for Fisher’s linear discriminant function, ‘naive bayes’, and some alternatives when there are many more variables than observations, Bernoulli, 10, 989-1010 (2004) · Zbl 1064.62073 |
| [4] | Cai, T.; Liu, W., A direct estimation approach to sparse linear discriminant analysis, J. Amer. Statist. Assoc., 106, 1566-1577 (2011) · Zbl 1233.62129 |
| [6] | Candes, E.; Tao, T., The dantzig selector: statistical estimation when p is much larger than n, Ann. Statist., 35, 2313-2351 (2007) · Zbl 1139.62019 |
| [7] | Danaher, P.; Wang, P.; Witten, D. M., The joint graphical lasso for inverse covariance estimation across multiple classes, J. R. Stat. Soc. Ser. B Stat. Methodol., 76, 373-397 (2014) · Zbl 07555455 |
| [8] | Fan, J.; Fan, Y., High dimensional classification using features annealed independence rules, Ann. Statist., 36, 2605-2637 (2008) · Zbl 1360.62327 |
| [9] | Fan, J.; Feng, Y.; Tong, X., A road to classification in high dimensional space: the regularized optimal affine discriminant, J. R. Stat. Soc. Ser. B Stat. Methodol., 74, 745-771 (2012) · Zbl 1411.62167 |
| [10] | Han, F.; Liu, H., High dimensional semiparametric scale-invariant principal component analysis, IEEE Trans. Pattern Anal. Mach. Intell., 36, 2016-2032 (2014) |
| [11] | Han, F.; Zhao, T.; Liu, H., Coda: High dimensional copula discriminant analysis, J. Mach. Learn. Res., 14, 629-671 (2013) · Zbl 1320.62145 |
| [12] | Hao, N.; Dong, B.; Fan, J., Sparsifying the Fisher linear discriminant by rotation, J. R. Stat. Soc. Ser. B Stat. Methodol., 77, 827-851 (2015) · Zbl 1414.62244 |
| [13] | Johnstone, I. M., On the distribution of the largest eigenvalue in principal components analysis, Ann. Statist., 295-327 (2001) · Zbl 1016.62078 |
| [14] | Johnstone, I. M.; Lu, A. Y., On consistency and sparsity for principal components analysis in high dimensions, J. Amer. Statist. Assoc. (2012) |
| [15] | Liu, H.; Han, F.; Yuan, M.; Lafferty, J.; Wasserman, L., High-dimensional semiparametric gaussian copula graphical models, Ann. Statist., 40, 2293-2326 (2012) · Zbl 1297.62073 |
| [16] | Liu, H.; Lafferty, J.; Wasserman, L., The nonparanormal: Semiparametric estimation of high dimensional undirected graphs, J. Mach. Learn. Res., 10, 2295-2328 (2009) · Zbl 1235.62035 |
| [18] | Mai, Q.; Zou, H.; Yuan, M., A direct approach to sparse discriminant analysis in ultra-high dimensions, Biometrika, 99, 29-42 (2012) · Zbl 1437.62550 |
| [20] | Trendafilov, N. T.; Jolliffe, I. T., Dalass: Variable selection in discriminant analysis via the lasso, Comput. Statist. Data Anal., 51, 3718-3736 (2007) · Zbl 1161.62379 |
| [21] | Wang, S.; Zhu, J., Improved centroids estimation for the nearest shrunken centroid classifier, Bioinformatics, 23, 972-979 (2007) |
| [22] | Wu, M. C.; Zhang, L.; Wang, Z.; Christiani, D. C.; Lin, X., Sparse linear discriminant analysis for simultaneous testing for the significance of a gene set/pathway and gene selection, Bioinformatics, 25, 1145-1151 (2009) |
| [23] | Yuan, M., High dimensional inverse covariance matrix estimation via linear programming, J. Mach. Learn. Res., 11, 2261-2286 (2010) · Zbl 1242.62043 |
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.
