# Sparse PCA with False Discovery Rate Controlled Variable Selection

arXiv: https://arxiv.org/abs/2401.08375 · HTML: https://mlsanity.com/paper/2401.08375/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 24 references that are in the map.
- First posted on arXiv 16 Jan 2024.

## Builds on (most cited first, 5 of 5)

- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [The Terminating-Random Experiments Selector: Fast High-Dimensional Variable Selection with False Discovery Rate Control](https://mlsanity.com/paper/2110.06048/) (2021)
- [Orthogonal Sparse PCA and Covariance Estimation via Procrustes Reformulation](https://mlsanity.com/paper/1602.03992/) (2016)
- [Sparse Principal Component Analysis via Rotation and Truncation](https://mlsanity.com/paper/1403.1430/) (2014)

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

- [FDR-Controlled Portfolio Optimization for Sparse Financial Index Tracking](https://mlsanity.com/paper/2401.15139/) (2024)
- [High-Dimensional False Discovery Rate Control for Dependent Variables](https://mlsanity.com/paper/2401.15796/) (2024)
- [Knockoff-Guided Compressive Sensing: A Statistical Machine Learning Framework for Support-Assured Signal Recovery](https://mlsanity.com/paper/2505.24727/) (2025)
- [Virtual Dummies: Enabling Scalable FDR-Controlled Variable Selection via Sequential Sampling of Null Features](https://mlsanity.com/paper/2604.07464/) (2026)

## Abstract (arXiv)

Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection. Sparse PCA algorithms are usually expressed as a trade-off between explained variance and sparsity of the loading vectors (i.e., number of selected variables). As a high explained variance is not necessarily synonymous with relevant information, these methods are prone to select irrelevant variables. To overcome this issue, we propose an alternative formulation of sparse PCA driven by the false discovery rate (FDR). We then leverage the Terminating-Random Experiments (T-Rex) selector to automatically determine an FDR-controlled support of the loading vectors. A major advantage of the resulting T-Rex PCA is that no sparsity parameter tuning is required. Numerical experiments and a stock market data example demonstrate a significant performance improvement.