Consistent selection of tuning parameters via variable selection stability

Abstract

Penalized regression models are popularly used in high-dimensional data analysis to conduct variable selection and model fitting simultaneously. Whereas success has been widely reported in literature, their performances largely depend on the tuning parameters that balance the trade-off between model fitting and model sparsity. Existing tuning criteria mainly follow the route of minimizing the estimated prediction error or maximizing the posterior model probability, such as cross-validation, AIC and BIC. This article introduces a general tuning parameter selection criterion based on a novel concept of variable selection stability. The key idea is to select the tuning parameters so that the resultant penalized regression model is stable in variable selection. The asymptotic selection consistency is established for both fixed and diverging dimensions. The effectiveness of the proposed criterion is also demonstrated in a variety of simulated examples as well as an application to the prostate cancer data.

Published in JMLR (http://jmlr.org/papers/v14/)

References in corpus (4)

• On the "degrees of freedom" of the lasso
• On the adaptive elastic-net with a diverging number of parameters
• Statistical Challenges with High Dimensionality: Feature Selection in Knowledge Discovery
• Asymptotic oracle properties of SCAD-penalized least squares estimators

Cited by in corpus (9)

• The iterative reweighted Mixed-Norm Estimate for spatio-temporal MEG/EEG source reconstruction
• Interpretable Models for Granger Causality Using Self-explaining Neural Networks
• Penalized Weighted Least Squares for Outlier Detection and Robust Regression
• New developments in Sparse PLS regression
• Provable Sparse Tensor Decomposition
• Variable selection using pseudo-variables
• Stabilized Sparse Online Learning for Sparse Data
• Stability Enhanced Large-Margin Classifier Selection
• Structure learning via unstructured kernel-based M-regression