Hybrid Denoising-screening for High-dimensional Contaminated Data

Feature screening is an effective tool to eliminate irrelevant features in high-dimensional analysis.When a high-dimensional dataset is contaminated with noisy observations, the conventional screening methods may lead to a poor screening accuracy.To tackle this problem, one practical strategy is to remove noisy observations and irrelevant features simultaneously.In this paper, we propose a novel hybrid denoising-screening (HDS) procedure for high-dimensional contaminated data.The new method is built upon a dual sample-feature L0 fitting procedure, which precisely controls both numbers of observations and features to be retained for the analysis.In the HDS process, only clean observations are selected and the joint effects between features are naturally accounted.These merits give HDS an edge to outperform the existing screening methods when faced with contaminated data.The promising performance of the method is supported by both theories and numerical examples.