Penalized Generative Variable Selection

TL;DR

This paper introduces a novel method combining Wasserstein GANs with Group Lasso penalization for variable selection in high-dimensional data, including censored survival data, improving model estimation, interpretability, and stability.

Contribution

It advances the field by integrating variable selection into deep generative models and extending analysis to censored survival data with proven convergence rates.

Findings

Effective variable selection in high-dimensional settings.

Improved distribution estimation for censored survival data.

Demonstrated practical utility through simulations and real data.

Abstract

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.