A0766
Title: Dynamic linear discriminant analysis in high dimensional space
Authors: Binyan Jiang - The Hong Kong Polytechnic University (Hong Kong) [presenting]
Ziqi Chen - Central South University (China)
Chenlei Leng - University of Warwick (United Kingdom)
Abstract: High-dimensional data that evolve dynamically feature predominantly in the modern data era. As a partial response to this, recent years have seen increasing emphasis to address the dimensionality challenge. However, the non-static nature of these datasets is largely ignored. Both challenges are addressed by proposing a novel yet simple dynamic linear programming discriminant (DLPD) rule for binary classification. Different from the usual static linear discriminant analysis, the new method is able to capture the changing distributions of the underlying populations by modeling their means and covariances as smooth functions of covariates of interest. Under an approximate sparse condition, we show that the conditional misclassification rate of the DLPD rule converges to the Bayes risk in probability uniformly over the range of the variables used for modeling the dynamics, even when the dimensionality is allowed to grow exponentially with the sample size. Minimax lower bound for the estimation of the Bayes risk is also established, which implies that the misclassification rate of our proposed rule is minimax-rate optimal. The promising performance of the DLPD rule is illustrated via extensive simulation studies and the analysis of a breast cancer dataset.
