Correlations and Copulas for Decision and Risk Analysis
Management Science
On Model Selection Consistency of Lasso
The Journal of Machine Learning Research
IEEE Transactions on Information Theory
The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs
The Journal of Machine Learning Research
High Dimensional Inverse Covariance Matrix Estimation via Linear Programming
The Journal of Machine Learning Research
The huge package for high-dimensional undirected graph estimation in R
The Journal of Machine Learning Research
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We propose a high dimensional classification method, named the Copula Discriminant Analysis (CODA). The CODA generalizes the normal-based linear discriminant analysis to the larger Gaussian Copula models (or the nonparanormal) as proposed by Liu et al. (2009). To simultaneously achieve estimation efficiency and robustness, the nonparametric rank-based methods including the Spearman's rho and Kendall's tau are exploited in estimating the covariance matrix. In high dimensional settings, we prove that the sparsity pattern of the discriminant features can be consistently recovered with the parametric rate, and the expected misclassification error is consistent to the Bayes risk. Our theory is backed up by careful numerical experiments, which show that the extra flexibility gained by the CODA method incurs little efficiency loss even when the data are truly Gaussian. These results suggest that the CODA method can be an alternative choice besides the normal-based high dimensional linear discriminant analysis.