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Abstract:
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Feature screening is crucial in analysis of ultrahigh dimensional data, where the number of variables (features) is exponentially larger than the number of observations. In various ultrahigh dimensional data, variables are naturally grouped and have correlation within the group. In this article, we propose a new feature screening method for data with grouped variables. This is in sharp contrast with existing literature on feature screening, which screens the variables individually. Under mild technical conditions, we show that the group screening procedure possesses a sure screening property that is defined by Fan and Lv (2008) while it nicely controls the false positive rate. We conduct finite sample simulations to demonstrate the advantages of the proposed method and apply it in analysis of a pharmacogenomics data set.
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