  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.
