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QING MAI - Florida State University

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Semiparametric Sparse Discriminant Analysis in High Dimensions
26 September 2013 from 4:00 PM to 5:00 PM
201 Thomas Bldg.
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In recent years, a considerable amount of work has been devoted to generalizing linear discriminant analysis to overcome its incompetence for high-dimensional classification (Tibshirani et al. (2002), Fan & Fan (2008), Wu et al. (2009), Clemmensen et al.  (2011), Cai & Liu (2011), Witten & Tibshirani (2011), Fan et al. (2012) and Mai et al. (2012)).  These research efforts are rejuvenating discriminant analysis. However, the normality assumption, which rarely holds in real applications, is still required by all of these recent methods. We develop high-dimensional semiparametric sparse discriminant analysis (SeSDA) that generalizes the normality-based discriminant analysis by relaxing the Gaussian assumption. If the underlying Bayes rule is sparse, SeSDA can estimate the Bayes rule and select the true features simultaneously with overwhelming probability, as long as the logarithm of dimension grows slower than the cube root of sample size. At the core of the theory is a new exponential concentration bound for semiparametric Gaussian copulas, which is of independent interest. Further, the analysis of a malaria data (Ockenhouse et al. (2006)) by SeSDA confirms the superior performance of SeSDA to normality-based methods in both classification and feature selection.