CODA: High dimensional Copula Discriminant Analysis

Fang Han, Tuo Zhao, Han Liu

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)629-671
Number of pages43
JournalJournal of Machine Learning Research
Issue number1
StatePublished - Feb 2013

All Science Journal Classification (ASJC) codes

  • Software
  • Artificial Intelligence
  • Control and Systems Engineering
  • Statistics and Probability


  • Gaussian Copula
  • High dimensional statistics
  • Nonparanormal distribution
  • Rank-based statistics
  • Sparse nonlinear discriminant analysis


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