Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914631822344192 |
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| author | Sanz-Alonso, Daniel Waniorek, Nathan |
| author_facet | Sanz-Alonso, Daniel Waniorek, Nathan |
| contents | This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain non-asymptotic bounds on the reconstruction error attained by maximum a posteriori estimators. The new theory explains how hierarchical Bayesian models that exploit sparsity, group sparsity, and sparse representations of the unknown parameter can achieve accurate reconstructions in high-dimensional settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03074 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint Sanz-Alonso, Daniel Waniorek, Nathan Statistics Theory Numerical Analysis 65M32, 62C10, 65F22 This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain non-asymptotic bounds on the reconstruction error attained by maximum a posteriori estimators. The new theory explains how hierarchical Bayesian models that exploit sparsity, group sparsity, and sparse representations of the unknown parameter can achieve accurate reconstructions in high-dimensional settings. |
| title | Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint |
| topic | Statistics Theory Numerical Analysis 65M32, 62C10, 65F22 |
| url | https://arxiv.org/abs/2401.03074 |