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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.02084 |
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| _version_ | 1866915370118414336 |
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| author | Feng, Yining Selesnick, Ivan |
| author_facet | Feng, Yining Selesnick, Ivan |
| contents | The adaptive Iterative Soft-Thresholding Algorithm (ISTA) has been a popular algorithm for finding a desirable solution to the LASSO problem without explicitly tuning the regularization parameter $λ$. Despite that the adaptive ISTA is a successful practical algorithm, few theoretical results exist. In this paper, we present the theoretical analysis on the adaptive ISTA with the thresholding strategy of estimating noise level by median absolute deviation. We show properties of the fixed points of the algorithm, including scale equivariance, non-uniqueness, and local stability, prove the local linear convergence guarantee, and show its global convergence behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02084 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive Iterative Soft-Thresholding Algorithm with the Median Absolute Deviation Feng, Yining Selesnick, Ivan Machine Learning Signal Processing The adaptive Iterative Soft-Thresholding Algorithm (ISTA) has been a popular algorithm for finding a desirable solution to the LASSO problem without explicitly tuning the regularization parameter $λ$. Despite that the adaptive ISTA is a successful practical algorithm, few theoretical results exist. In this paper, we present the theoretical analysis on the adaptive ISTA with the thresholding strategy of estimating noise level by median absolute deviation. We show properties of the fixed points of the algorithm, including scale equivariance, non-uniqueness, and local stability, prove the local linear convergence guarantee, and show its global convergence behavior. |
| title | Adaptive Iterative Soft-Thresholding Algorithm with the Median Absolute Deviation |
| topic | Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2507.02084 |