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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.02607 |
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| _version_ | 1866912256278659072 |
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| author | Nagano, Yasushi Hukushima, Koji |
| author_facet | Nagano, Yasushi Hukushima, Koji |
| contents | In sparse signal processing, this study investigates the effect of the global shrinkage parameter $τ$ of a horseshoe prior, one of the global-local shrinkage prior, on the linear regression. Statistical mechanics methods are employed to examine the accuracy of signal estimation. A phase diagram of successful and failure of signal recovery in noise-less compressed sensing with varying $τ$ is discussed from the viewpoint of dynamic characterization of the approximate message passing as a solving algorithm and static characterization of the free-energy landscape. It is found that there exists a parameter region where the approximate message passing algorithm can hardly recover the true signal, even though the true signal is locally stable. The analysis of the free-energy landscape also provides important insight into the optimal choice of $τ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_02607 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Effect of global shrinkage parameter of horseshoe prior in compressed sensing Nagano, Yasushi Hukushima, Koji Disordered Systems and Neural Networks In sparse signal processing, this study investigates the effect of the global shrinkage parameter $τ$ of a horseshoe prior, one of the global-local shrinkage prior, on the linear regression. Statistical mechanics methods are employed to examine the accuracy of signal estimation. A phase diagram of successful and failure of signal recovery in noise-less compressed sensing with varying $τ$ is discussed from the viewpoint of dynamic characterization of the approximate message passing as a solving algorithm and static characterization of the free-energy landscape. It is found that there exists a parameter region where the approximate message passing algorithm can hardly recover the true signal, even though the true signal is locally stable. The analysis of the free-energy landscape also provides important insight into the optimal choice of $τ$. |
| title | Effect of global shrinkage parameter of horseshoe prior in compressed sensing |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2306.02607 |