Computer Science > Information Theory
arXiv:2408.06907 (cs)
[Submitted on 13 Aug 2024]
Title:An Information Geometry Interpretation for Approximate Message Passing
View a PDF of the paper titled An Information Geometry Interpretation for Approximate Message Passing, by Bingyan Liu and 4 other authors
View PDFHTML (experimental)Abstract:In this paper, we propose an information geometry (IG) framework to solve the standard linear regression problem. The proposed framework is an extension of the one for computing the mean of complex multivariate Gaussian distribution. By applying the proposed framework, the information geometry approach (IGA) and the approximate information geometry approach (AIGA) for basis pursuit de-noising (BPDN) in standard linear regression are derived. The framework can also be applied to other standard linear regression problems. With the transformations of natural and expectation parameters of Gaussian distributions, we then show the relationship between the IGA and the message passing (MP) algorithm. Finally, we prove that the AIGA is equivalent to the approximate message passing (AMP) algorithm. These intrinsic results offer a new perspective for the AMP algorithm, and clues for understanding and improving stochastic reasoning methods.
| Comments: | 30 pages, 5 figures |
| Subjects: | Information Theory (cs.IT) |
| Cite as: | arXiv:2408.06907 [cs.IT] |
| (orarXiv:2408.06907v1 [cs.IT] for this version) | |
| https://doi.org/10.48550/arXiv.2408.06907 arXiv-issued DOI via DataCite |
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View a PDF of the paper titled An Information Geometry Interpretation for Approximate Message Passing, by Bingyan Liu and 4 other authors
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