Varying Coefficient Linear Discriminant Analysis for Dynamic Data

Linear discriminant analysis (LDA) is a vital classification tool in statistics and machine learning. This paper investigates the varying coefficient LDA model for dynamic data, with Bayes' discriminant direction being a function of some exposure variable to address the heterogeneity. By deriving a new discriminant direction function parallel with Bayes' direction, we propose a least-square estimation procedure based on the B-spline approximation. For high-dimensional regime, the corresponding data-driven discriminant rule is more computationally efficient than the existed dynamic linear programming rule. We also establish the corresponding theoretical results, including estimation error bound and the uniform excess misclassification rate. Numerical experiments on synthetic data and real data both corroborate the superiority of our proposed classification method.