B0486
Title: High dimensional linear discriminant analysis: Locally-adaptive shrinkage estimation and false selection rate control
Authors: Bowen Gang - Fudan University (China) [presenting]
Wenguang Sun - University of Southern California (United States)
Abstract: The focus is on the problem of controlling error rate in high dimensional linear discriminant analysis. The problem has two major challenges. First, the oracle Fisher's rule cannot guarantee a low error rate. Second, existing methods for accurate estimation of significance index in high dimensional setting either require strong assumptions that may not hold in practice or have little theoretical support. To address the first challenge, we propose to control a generalization of misclassification rate called false selection rate (FSR). For the second challenge, we propose a locally adaptive shrinkage approach to estimate the class probabilities. In contrast to existing methods, our proposed method does not require the usual sparsity or independence assumptions. The new method is shown to have desirable theoretical properties and reveals an interesting dynamic between estimating discriminant and estimating class probabilities. The numerical performance of the classifier is investigated using both simulated and real data. In particular, the procedure is applied to analyze a lung cancer dataset and is found to perform favorably compared with existing methods.
