# Knockoff-Guided Compressive Sensing: A Statistical Machine Learning Framework for Support-Assured Signal Recovery

arXiv: https://arxiv.org/abs/2505.24727 · HTML: https://mlsanity.com/paper/2505.24727/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 39 references that are in the map.
- First posted on arXiv 30 May 2025.

## Builds on (most cited first, 14 of 14)

- [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)
- [Deep Knockoffs](https://mlsanity.com/paper/1811.06687/) (2018)
- [A knockoff filter for high-dimensional selective inference](https://mlsanity.com/paper/1602.03574/) (2016)
- [Compression Boosts Differentially Private Federated Learning](https://mlsanity.com/paper/2011.05578/) (2020)
- [Derandomized knockoffs: leveraging e-values for false discovery rate control](https://mlsanity.com/paper/2205.15461/) (2022)
- [The knockoff filter for FDR control in group-sparse and multitask regression](https://mlsanity.com/paper/1602.03589/) (2016)
- [Controlling False Discovery Rate Using Gaussian Mirrors](https://mlsanity.com/paper/1911.09761/) (2019)
- [The Terminating-Random Experiments Selector: Fast High-Dimensional Variable Selection with False Discovery Rate Control](https://mlsanity.com/paper/2110.06048/) (2021)
- [Sparse PCA with False Discovery Rate Controlled Variable Selection](https://mlsanity.com/paper/2401.08375/) (2024)
- [Controlling the False Discovery Rate in Transformational Sparsity: Split Knockoffs](https://mlsanity.com/paper/2103.16159/) (2021)
- [Controlling the FDR in variable selection via multiple knockoffs](https://mlsanity.com/paper/1911.09442/) (2019)
- [Robust Deep Compressive Sensing with Recurrent-Residual Structural Constraints](https://mlsanity.com/paper/2207.07301/) (2022)
- [Knoop: Practical Enhancement of Knockoff with Over-Parameterization for Variable Selection](https://mlsanity.com/paper/2501.17889/) (2025)

## Abstract (arXiv)

This paper introduces a novel Knockoff-guided compressive sensing framework, referred to as TheName, which enhances signal recovery by leveraging precise false discovery rate (FDR) control during the support identification phase. Unlike LASSO, which jointly performs support selection and signal estimation without explicit error control, our method guarantees FDR control in finite samples, enabling more reliable identification of the true signal support. By separating and controlling the support recovery process through statistical Knockoff filters, our framework achieves more accurate signal reconstruction, especially in challenging scenarios where traditional methods fail. We establish theoretical guarantees demonstrating how FDR control directly ensures recovery performance under weaker conditions than traditional ℓ1-based compressive sensing methods, while maintaining accurate signal reconstruction. Extensive numerical experiments demonstrate that our proposed Knockoff-based method consistently outperforms LASSO-based and other state-of-the-art compressive sensing techniques. In simulation studies, our method improves F1-score by up to 3.9x over baseline methods, attributed to principled false discovery rate (FDR) control and enhanced support recovery. The method also consistently yields lower reconstruction and relative errors. We further validate the framework on real-world datasets, where it achieves top downstream predictive performance across both regression and classification tasks, often narrowing or even surpassing the performance gap relative to uncompressed signals. These results establish TheName as a robust and practical alternative to existing approaches, offering both theoretical guarantees and strong empirical performance through statistically grounded support selection.