# Penalized Generative Variable Selection

arXiv: https://arxiv.org/abs/2402.16661 · HTML: https://mlsanity.com/paper/2402.16661/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 42 references that are in the map.
- First posted on arXiv 26 Feb 2024.

## Builds on (most cited first, 8 of 8)

- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [LassoNet: A Neural Network with Feature Sparsity](https://mlsanity.com/paper/1907.12207/) (2019)
- [Sparse-Input Neural Networks for High-dimensional Nonparametric Regression and Classification](https://mlsanity.com/paper/1711.07592/) (2017)
- [Consistent Feature Selection for Analytic Deep Neural Networks](https://mlsanity.com/paper/2010.08097/) (2020)
- [Wasserstein Generative Learning of Conditional Distribution](https://mlsanity.com/paper/2112.10039/) (2021)
- [A Universal Approximation Theorem of Deep Neural Networks for Expressing Probability Distributions](https://mlsanity.com/paper/2004.08867/) (2020)
- [Sparse-Input Neural Network using Group Concave Regularization](https://mlsanity.com/paper/2307.00344/) (2023)
- [Estimation of Non-Crossing Quantile Regression Process with Deep ReQU Neural Networks](https://mlsanity.com/paper/2207.10442/) (2022)

## Built on by (most cited first, 1 of 1)

- [Minimal Sufficient Representations for Self-interpretable Deep Neural Networks](https://mlsanity.com/paper/2603.24041/) (2026)

## Abstract (arXiv)

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.