Consistent selection of tuning parameters via variable selection stability

TL;DR

This paper proposes a new method for selecting tuning parameters in penalized regression models by focusing on the stability of variable selection, ensuring consistent model selection in high-dimensional settings.

Contribution

It introduces a novel stability-based tuning criterion with proven asymptotic consistency for both fixed and diverging dimensions.

Findings

The proposed criterion achieves consistent variable selection asymptotically.

Simulation studies demonstrate the effectiveness of the stability-based method.

Application to prostate cancer data illustrates practical utility.

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.