Quadratic discriminant analysis in distributed frameworks
Bin Du, Shengbin Zheng, Junlong Zhao · Statistics · 2025
Quadratic discriminant analysis (QDA) is a useful tool for binary classification problems. We focus on QDA in distributed frameworks where n observations are distributed on k local sites and cannot be merged. Supposing that the predictors are of dimension p, to compute the centralized QDA, p by p local summary matrices need to be transmitted, which is undesirable when transmission costs or privacy protection is concerned. To solve the problem, the divide-and-conquer (DC) approach can be applied by aggregating the local QDA on each site. Although DC estimator is efficient in communication costs, theoretical results reveal that the DC estimator requires strong conditions on p or k that fail when p or k is large. To fix this problem, we propose an alternative distributed QDA that requires the similar communication costs as DC estimator and achieves the same misclassification rate as the centralized QDA asymptotically under weaker conditions.