Tuning-Free Structured Sparse Recovery of Multiple Measurement Vectors using Implicit Regularization
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| author | Jayalal, Lakshmi Kalyani, Sheetal |
| author_facet | Jayalal, Lakshmi Kalyani, Sheetal |
| contents | Recovering jointly sparse signals in the multiple measurement vectors (MMV) setting is a fundamental problem in machine learning, but traditional methods often require careful parameter tuning or prior knowledge of the sparsity of the signal and/or noise variance. We propose a tuning-free framework that leverages implicit regularization (IR) from overparameterization to overcome this limitation. Our approach reparameterizes the estimation matrix into factors that decouple the shared row-support from individual vector entries and applies gradient descent to a standard least-squares objective. We prove that with a sufficiently small and balanced initialization, the optimization dynamics exhibit a "momentum-like" effect where the true support grows significantly faster. Leveraging a Lyapunov-based analysis of the gradient flow, we further establish formal guarantees that the solution trajectory converges towards an idealized row-sparse solution. Empirical results demonstrate that our tuning-free approach achieves performance comparable to optimally tuned established methods. Furthermore, our framework significantly outperforms these baselines in scenarios where accurate priors are unavailable to the baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03393 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tuning-Free Structured Sparse Recovery of Multiple Measurement Vectors using Implicit Regularization Jayalal, Lakshmi Kalyani, Sheetal Machine Learning Recovering jointly sparse signals in the multiple measurement vectors (MMV) setting is a fundamental problem in machine learning, but traditional methods often require careful parameter tuning or prior knowledge of the sparsity of the signal and/or noise variance. We propose a tuning-free framework that leverages implicit regularization (IR) from overparameterization to overcome this limitation. Our approach reparameterizes the estimation matrix into factors that decouple the shared row-support from individual vector entries and applies gradient descent to a standard least-squares objective. We prove that with a sufficiently small and balanced initialization, the optimization dynamics exhibit a "momentum-like" effect where the true support grows significantly faster. Leveraging a Lyapunov-based analysis of the gradient flow, we further establish formal guarantees that the solution trajectory converges towards an idealized row-sparse solution. Empirical results demonstrate that our tuning-free approach achieves performance comparable to optimally tuned established methods. Furthermore, our framework significantly outperforms these baselines in scenarios where accurate priors are unavailable to the baselines. |
| title | Tuning-Free Structured Sparse Recovery of Multiple Measurement Vectors using Implicit Regularization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2512.03393 |