A review of quadratic discriminant analysis for high-dimensional data

Quadratic discriminant analysis (QDA) is a classical and flexible classification approach, which allows differences between groups not only due to mean vectors but also covariance matrices. Modern high-dimensional data bring us opportunities and also challenges. In the framework of classical QDA, the inverse of each sample covariance matrix is essential, but high-dimensionality causes singularity in sample covariance matrices. To overcome this technical difficulty, several high-dimensional QDA approaches with desirable theoretical properties emerge in recent years. We are to discuss the challenges, some existing works, and possibly several future directions with regard to high-dimensional QDA.