An Adaptive Ridge Procedure for L0 Regularization
Penalized selection criteria like AIC or BIC are among the most popular methods for variable selection. Their theoretical properties have been studied intensively and are well understood, but making use of them in case of high-dimensional data is difficult due to the non-convex optimization problem...
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| Veröffentlicht in: | PloS one 2016-02, Vol.11 (2), p.e0148620-e0148620 |
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| description | Penalized selection criteria like AIC or BIC are among the most popular methods for variable selection. Their theoretical properties have been studied intensively and are well understood, but making use of them in case of high-dimensional data is difficult due to the non-convex optimization problem induced by L0 penalties. In this paper we introduce an adaptive ridge procedure (AR), where iteratively weighted ridge problems are solved whose weights are updated in such a way that the procedure converges towards selection with L0 penalties. After introducing AR its specific shrinkage properties are studied in the particular case of orthogonal linear regression. Based on extensive simulations for the non-orthogonal case as well as for Poisson regression the performance of AR is studied and compared with SCAD and adaptive LASSO. Furthermore an efficient implementation of AR in the context of least-squares segmentation is presented. The paper ends with an illustrative example of applying AR to analyze GWAS data. |
| doi_str_mv | 10.1371/journal.pone.0148620 |
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| subjects | Algorithms Biology and Life Sciences Computer and Information Sciences Convex analysis Convexity Data processing Economic models Estimates Fines & penalties Genomes Haplotypes Models, Theoretical Optimization Physical Sciences Poisson density functions Regression analysis Regularization Regularization methods Research and Analysis Methods Segmentation Shrinkage Sparsity Statistical analysis Studies |
| title | An Adaptive Ridge Procedure for L0 Regularization |
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