# Semiparametric Sparse Discriminant Analysis

arXiv: https://arxiv.org/abs/1304.4983 · HTML: https://mlsanity.com/paper/1304.4983/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2013.

## Built on by (most cited first, 2 of 2)

- [Linear Discriminant Analysis with High-dimensional Mixed Variables](https://mlsanity.com/paper/2112.07145/) (2021)
- [Varying Coefficient Linear Discriminant Analysis for Dynamic Data](https://mlsanity.com/paper/2203.06371/) (2022)

## Abstract (arXiv)

In recent years, a considerable amount of work has been devoted to generalizing linear discriminant analysis to overcome its incompetence for high-dimensional classification (Witten & Tibshirani 2011, Cai & Liu 2011, Mai et al. 2012, Fan et al. 2012). In this paper, we develop high-dimensional semiparametric sparse discriminant analysis (HD-SeSDA) that generalizes the normal-theory discriminant analysis in two ways: it relaxes the Gaussian assumptions and can handle non-polynomial (NP) dimension classification problems. If the underlying Bayes rule is sparse, HD-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. Simulated and real examples are used to demonstrate the finite sample performance of HD-SeSDA. At the core of the theory is a new exponential concentration bound for semiparametric Gaussian copulas, which is of independent interest.