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

2025-05-30

AI Summary

In compressed sensing, unreliable signal recovery arises when the false discovery rate (FDR) in support set identification becomes uncontrolled. Method: This paper introduces the first framework integrating statistical knockoff methods into compressed sensing, enabling rigorous finite-sample FDR control. It decouples support selection from signal estimation via knockoff variable construction, the knockoff+ thresholding rule, and sparse modeling. Contribution/Results: The method achieves theoretically guaranteed FDR control—the first such result in compressed sensing—and significantly enhances robustness under challenging regimes (e.g., small sample sizes, high feature correlations). Experiments demonstrate up to a 3.9× improvement in F1-score, systematic reductions in reconstruction and relative errors, and downstream regression/classification performance on real data that matches or surpasses that achieved using the original uncompressed signals.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Data Mining & Knowledge Management: Data Compression
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

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 $ell_1$-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.

Problem

• Enhances signal recovery with precise FDR control
• Guarantees FDR control in finite samples
• Improves accuracy in challenging recovery scenarios

Innovation

• Knockoff filters ensure precise FDR control
• Separates support recovery for accurate reconstruction
• Outperforms LASSO with better F1-scores