# Error Controlled Feature Selection for Ultrahigh Dimensional and Highly Correlated Feature Space Using Deep Learning

arXiv: https://arxiv.org/abs/2209.07011 · HTML: https://mlsanity.com/paper/2209.07011/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 58 references that are in the map.
- First posted on arXiv 15 Sep 2022.

## Builds on (most cited first, 19 of 19)

- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Deep Neural Network Approximation Theory](https://mlsanity.com/paper/1901.02220/) (2019)
- [LassoNet: A Neural Network with Feature Sparsity](https://mlsanity.com/paper/1907.12207/) (2019)
- [DeepPINK: reproducible feature selection in deep neural networks](https://mlsanity.com/paper/1809.01185/) (2018)
- [Deep Knockoffs](https://mlsanity.com/paper/1811.06687/) (2018)
- [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)
- [On the Non-asymptotic and Sharp Lower Tail Bounds of Random Variables](https://mlsanity.com/paper/1810.09006/) (2018)
- [High-Dimensional Inference: Confidence Intervals, p-Values and R-Software hdi](https://mlsanity.com/paper/1408.4026/) (2014)
- [AdaPT: An interactive procedure for multiple testing with side information](https://mlsanity.com/paper/1609.06035/) (2016)
- [Robust inference with knockoffs](https://mlsanity.com/paper/1801.03896/) (2018)
- [Gene Hunting with Knockoffs for Hidden Markov Models](https://mlsanity.com/paper/1706.04677/) (2017)
- [Multiple testing with the structure adaptive Benjamini-Hochberg algorithm](https://mlsanity.com/paper/1606.07926/) (2016)
- [NeuralFDR: Learning Discovery Thresholds from Hypothesis Features](https://mlsanity.com/paper/1711.01312/) (2017)
- [Black Box FDR](https://mlsanity.com/paper/1806.03143/) (2018)
- [Variable selection with false discovery rate control in deep neural networks](https://mlsanity.com/paper/1909.07561/) (2019)
- [Random weighting in LASSO regression](https://mlsanity.com/paper/2002.02629/) (2020)
- [Distributional Consistency of Lasso by Perturbation Bootstrap](https://mlsanity.com/paper/1710.10709/) (2017)

## Abstract (arXiv)

In recent years, deep learning has been at the center of analytics due to its impressive empirical success in analyzing complex data objects. Despite this success, most of the existing tools behave like black-box machines, thus the increasing interest in interpretable, reliable, and robust deep learning models applicable to a broad class of applications. Feature-selected deep learning has emerged as a promising tool in this realm. However, the recent developments do not accommodate ultra-high dimensional and highly correlated features, in addition to the high noise level. In this article, we propose a novel screening and cleaning method with the aid of deep learning for a data-adaptive multi-resolutional discovery of highly correlated predictors with a controlled error rate. Extensive empirical evaluations over a wide range of simulated scenarios and several real datasets demonstrate the effectiveness of the proposed method in achieving high power while keeping the false discovery rate at a minimum.