Unifying AMP Algorithms for Rotationally-Invariant Models
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913594532167680 |
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| author | Liu, Songbin Ma, Junjie |
| author_facet | Liu, Songbin Ma, Junjie |
| contents | This paper presents a unified framework for constructing Approximate Message Passing (AMP) algorithms for rotationally-invariant models. By employing a general iterative algorithm template and reducing it to long-memory Orthogonal AMP (OAMP), we systematically derive the correct Onsager terms of AMP algorithms. This approach allows us to rederive an AMP algorithm introduced by Fan and Opper et al., while shedding new light on the role of free cumulants of the spectral law. The free cumulants arise naturally from a recursive centering operation, potentially of independent interest beyond the scope of AMP. To illustrate the flexibility of our framework, we introduce two novel AMP variants and apply them to estimation in spiked models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unifying AMP Algorithms for Rotationally-Invariant Models Liu, Songbin Ma, Junjie Statistics Theory Information Theory Machine Learning Probability This paper presents a unified framework for constructing Approximate Message Passing (AMP) algorithms for rotationally-invariant models. By employing a general iterative algorithm template and reducing it to long-memory Orthogonal AMP (OAMP), we systematically derive the correct Onsager terms of AMP algorithms. This approach allows us to rederive an AMP algorithm introduced by Fan and Opper et al., while shedding new light on the role of free cumulants of the spectral law. The free cumulants arise naturally from a recursive centering operation, potentially of independent interest beyond the scope of AMP. To illustrate the flexibility of our framework, we introduce two novel AMP variants and apply them to estimation in spiked models. |
| title | Unifying AMP Algorithms for Rotationally-Invariant Models |
| topic | Statistics Theory Information Theory Machine Learning Probability |
| url | https://arxiv.org/abs/2412.01574 |