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Abstract:
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The performances of penalized likelihood approaches profoundly depend on the selection of the tuning parameter, however there has not been a common agreement on the criterion for choosing the tuning parameter. Here we introduce a novel approach for feature selection based on the whole solution path rather than choosing one value for the tuning parameter, which significantly improves the selection accuracy. Moreover, it allows for feature selection using ridge or other strictly convex penalties. The key idea is to classify the variables as relevant or irrelevant for each tuning parameter and then select all the variables which have been classified as relevant at least once. We establish the theoretical properties of the method, and illustrate the advantages of the proposed approach with simulation studies and a data example.
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