Electronic Journal of Statistics

Selection by partitioning the solution paths

Yang Liu and Peng Wang

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The performance of penalized likelihood approaches depends profoundly on the selection of the tuning parameter; however, there is no commonly agreed-upon criterion for choosing the tuning parameter. Moreover, penalized likelihood estimation based on a single value of the tuning parameter suffers from several drawbacks. This article introduces a novel approach for feature selection based on the entire solution paths rather than the choice of a single tuning parameter, which significantly improves the accuracy of the selection. Moreover, the approach allows for feature selection using ridge or other strictly convex penalties. The key idea is to classify variables as relevant or irrelevant at each tuning parameter and then to select all of the variables which have been classified as relevant at least once. We establish the theoretical properties of the method, which requires significantly weaker conditions than existing methods in the literature. We also illustrate the advantages of the proposed approach with simulation studies and a data example.

Article information

Electron. J. Statist., Volume 12, Number 1 (2018), 1988-2017.

Received: January 2018
First available in Project Euclid: 18 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F07: Ranking and selection
Secondary: 62J07: Ridge regression; shrinkage estimators 62J86: Fuzziness, and linear inference and regression

Penalized likelihood lasso variable/feature selection solution paths AIC/BIC cross-validation tuning

Creative Commons Attribution 4.0 International License.


Liu, Yang; Wang, Peng. Selection by partitioning the solution paths. Electron. J. Statist. 12 (2018), no. 1, 1988--2017. doi:10.1214/18-EJS1434. https://projecteuclid.org/euclid.ejs/1529308885

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