# Ultra High-Dimensional Nonlinear Feature Selection for Big Biological Data

arXiv: https://arxiv.org/abs/1608.04048 · HTML: https://mlsanity.com/paper/1608.04048/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Aug 2016.

## Built on by (most cited first, 7 of 7)

- [Comprehensible Artificial Intelligence on Knowledge Graphs: A survey](https://mlsanity.com/paper/2404.03499/) (2024)
- [Deep Feature Screening: Feature Selection for Ultra High-Dimensional Data via Deep Neural Networks](https://mlsanity.com/paper/2204.01682/) (2022)
- [Graph Convolutional Network-based Feature Selection for High-dimensional and Low-sample Size Data](https://mlsanity.com/paper/2211.14144/) (2022)
- [LCEN: A Nonlinear, Interpretable Feature Selection and Machine Learning Algorithm](https://mlsanity.com/paper/2402.17120/) (2024)
- [ROOFS: RObust biOmarker Feature Selection](https://mlsanity.com/paper/2601.05151/) (2026)
- [Top-k Regularization for Supervised Feature Selection](https://mlsanity.com/paper/2106.02197/) (2021)
- [A Novel Multi-Timescale Stability-Preserving Hierarchical Reinforcement Learning Controller Framework for Adaptive Control in High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2510.22420/) (2025)

## Abstract (arXiv)

Machine learning methods are used to discover complex nonlinear relationships in biological and medical data. However, sophisticated learning models are computationally unfeasible for data with millions of features. Here we introduce the first feature selection method for nonlinear learning problems that can scale up to large, ultra-high dimensional biological data. More specifically, we scale up the novel Hilbert-Schmidt Independence Criterion Lasso (HSIC Lasso) to handle millions of features with tens of thousand samples. The proposed method is guaranteed to find an optimal subset of maximally predictive features with minimal redundancy, yielding higher predictive power and improved interpretability. Its effectiveness is demonstrated through applications to classify phenotypes based on module expression in human prostate cancer patients and to detect enzymes among protein structures. We achieve high accuracy with as few as 20 out of one million features --- a dimensionality reduction of 99.998%. Our algorithm can be implemented on commodity cloud computing platforms. The dramatic reduction of features may lead to the ubiquitous deployment of sophisticated prediction models in mobile health care applications.