Robust High-Dimensional Linear Discriminant Analysis under Training Data Contamination

The problem of robust Sparse Linear Discriminant Analysis (LDA) in high-dimensions is studied, in which a fraction of the training data may be corrupted by an adversary. A computationally efficient algorithm is proposed by adapting robust mean estimation along with a calibration framework for LDA. Theoretical properties of the proposed algorithm are established for both the estimation error of the optimal projection vector and the mis-classification rate. Results from extensive numerical studies on both synthetic and real datasets are reported to show the usefulness of our algorithm.