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.

翻译：深度网络越来越多地应用于各种数据类型，包括高维预测变量的数据。在此类分析中，变量选择可能与估计/模型构建同时需要。许多现有的融合变量选择的深度网络研究局限于方法论和数值层面的发展。在本研究中，我们考虑使用条件Wasserstein生成对抗网络进行建模/估计。应用组Lasso惩罚进行变量选择，这可以改善模型估计/预测、可解释性、稳定性等。相较于现有文献的重要进展是，我们还考虑了删失生存数据的分析。我们在考虑逼近误差的同时建立了变量选择的收敛速率，并获得了更有效的分布估计。模拟实验和真实实验数据分析证明了所提出分析方法的实用有效性。