Linear Operator Approximate Message Passing (OpAMP)
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911379779223552 |
|---|---|
| author | Rossetti, Riccardo Nazer, Bobak Reeves, Galen |
| author_facet | Rossetti, Riccardo Nazer, Bobak Reeves, Galen |
| contents | This paper introduces a framework for approximate message passing (AMP) in dynamic settings where the data at each iteration is passed through a linear operator. This framework is motivated in part by applications in large-scale, distributed computing where only a subset of the data is available at each iteration. An autoregressive memory term is used to mitigate information loss across iterations and a specialized algorithm, called projection AMP, is designed for the case where each linear operator is an orthogonal projection. Precise theoretical guarantees are provided for a class of Gaussian matrices and non-separable denoising functions. Specifically, it is shown that the iterates can be well-approximated in the high-dimensional limit by a Gaussian process whose second-order statistics are defined recursively via state evolution. These results are applied to the problem of estimating a rank-one spike corrupted by additive Gaussian noise using partial row updates, and the theory is validated by numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08225 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear Operator Approximate Message Passing (OpAMP) Rossetti, Riccardo Nazer, Bobak Reeves, Galen Statistics Theory Information Theory Probability This paper introduces a framework for approximate message passing (AMP) in dynamic settings where the data at each iteration is passed through a linear operator. This framework is motivated in part by applications in large-scale, distributed computing where only a subset of the data is available at each iteration. An autoregressive memory term is used to mitigate information loss across iterations and a specialized algorithm, called projection AMP, is designed for the case where each linear operator is an orthogonal projection. Precise theoretical guarantees are provided for a class of Gaussian matrices and non-separable denoising functions. Specifically, it is shown that the iterates can be well-approximated in the high-dimensional limit by a Gaussian process whose second-order statistics are defined recursively via state evolution. These results are applied to the problem of estimating a rank-one spike corrupted by additive Gaussian noise using partial row updates, and the theory is validated by numerical simulations. |
| title | Linear Operator Approximate Message Passing (OpAMP) |
| topic | Statistics Theory Information Theory Probability |
| url | https://arxiv.org/abs/2405.08225 |