Penalized Generative Variable Selection
This work addresses variable selection for high-dimensional data analysis, particularly in censored survival data, but is incremental as it builds on existing deep network methods with penalization.
The authors tackled variable selection in high-dimensional data using deep networks by applying Group Lasso penalization to conditional Wasserstein Generative Adversarial networks, achieving a more efficient distribution estimation and establishing convergence rates for variable selection, with simulations and real data showing satisfactory utility.
Deep networks are increasingly applied to a wide variety of data, including data with high-dimensional predictors. In such analysis, variable selection can be needed along with estimation/model building. Many of the existing deep network studies that incorporate variable selection have been limited to methodological and numerical developments. In this study, we consider modeling/estimation using the conditional Wasserstein Generative Adversarial networks. Group Lasso penalization is applied for variable selection, which may improve model estimation/prediction, interpretability, stability, etc. Significantly advancing from the existing literature, the analysis of censored survival data is also considered. We establish the convergence rate for variable selection while considering the approximation error, and obtain a more efficient distribution estimation. Simulations and the analysis of real experimental data demonstrate satisfactory practical utility of the proposed analysis.