# Deep neural networks with controlled variable selection for the identification of putative causal genetic variants

arXiv: https://arxiv.org/abs/2109.14719 · HTML: https://mlsanity.com/paper/2109.14719/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 73 references that are in the map.
- First posted on arXiv 29 Sep 2021.

## Builds on (most cited first, 12 of 12)

- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [DeepPINK: reproducible feature selection in deep neural networks](https://mlsanity.com/paper/1809.01185/) (2018)
- [Collapse of Deep and Narrow Neural Nets](https://mlsanity.com/paper/1808.04947/) (2018)
- [Tree-CNN: A Hierarchical Deep Convolutional Neural Network for Incremental Learning](https://mlsanity.com/paper/1802.05800/) (2018)
- [Interpretation of Prediction Models Using the Input Gradient](https://mlsanity.com/paper/1611.07634/) (2016)
- [False Discovery Rate Control via Data Splitting](https://mlsanity.com/paper/2002.08542/) (2020)
- [Derandomizing Knockoffs](https://mlsanity.com/paper/2012.02717/) (2020)
- [Improving the Stability of the Knockoff Procedure: Multiple Simultaneous Knockoffs and Entropy Maximization](https://mlsanity.com/paper/1810.11378/) (2018)
- [The Ramifications of Making Deep Neural Networks Compact](https://mlsanity.com/paper/2006.15098/) (2020)
- [Variable selection with false discovery rate control in deep neural networks](https://mlsanity.com/paper/1909.07561/) (2019)

## Built on by (most cited first, 4 of 4)

- [PRISM: Periodic Representation with multIscale and Similarity graph Modelling for enhanced crystal structure property prediction](https://mlsanity.com/paper/2511.20362/) (2025)
- [Interpreting artificial neural networks to detect genome-wide association signals for complex traits](https://mlsanity.com/paper/2407.18811/) (2024)
- [GRIP2: A Robust and Powerful Deep Knockoff Method for Feature Selection](https://mlsanity.com/paper/2602.00218/) (2026)
- [Knockoffs-based False Discovery Rate Control and Simplification for Deep Neural Networks](https://mlsanity.com/paper/2606.04404/) (2026)

## Abstract (arXiv)

Deep neural networks (DNN) have been used successfully in many scientific problems for their high prediction accuracy, but their application to genetic studies remains challenging due to their poor interpretability. In this paper, we consider the problem of scalable, robust variable selection in DNN for the identification of putative causal genetic variants in genome sequencing studies. We identified a pronounced randomness in feature selection in DNN due to its stochastic nature, which may hinder interpretability and give rise to misleading results. We propose an interpretable neural network model, stabilized using ensembling, with controlled variable selection for genetic studies. The merit of the proposed method includes: (1) flexible modelling of the non-linear effect of genetic variants to improve statistical power; (2) multiple knockoffs in the input layer to rigorously control false discovery rate; (3) hierarchical layers to substantially reduce the number of weight parameters and activations to improve computational efficiency; (4) de-randomized feature selection to stabilize identified signals. We evaluated the proposed method in extensive simulation studies and applied it to the analysis of Alzheimer disease genetics. We showed that the proposed method, when compared to conventional linear and nonlinear methods, can lead to substantially more discoveries.