Estimation in rotationally invariant generalized linear models via approximate message passing

Venkataramanan R, Kögler K, Mondelli M. 2022. Estimation in rotationally invariant generalized linear models via approximate message passing. Proceedings of the 39th International Conference on Machine Learning. ICML: International Conference on Machine Learning vol. 162, 22.

Download
OA 2022_PMLR_Venkataramanan.pdf 2.34 MB [Published Version]
Conference Paper | Published | English
Author
Venkataramanan, Ramji; Kögler, KevinISTA; Mondelli, MarcoISTA

Corresponding author has ISTA affiliation

Department
Abstract
We consider the problem of signal estimation in generalized linear models defined via rotationally invariant design matrices. Since these matrices can have an arbitrary spectral distribution, this model is well suited for capturing complex correlation structures which often arise in applications. We propose a novel family of approximate message passing (AMP) algorithms for signal estimation, and rigorously characterize their performance in the high-dimensional limit via a state evolution recursion. Our rotationally invariant AMP has complexity of the same order as the existing AMP derived under the restrictive assumption of a Gaussian design; our algorithm also recovers this existing AMP as a special case. Numerical results showcase a performance close to Vector AMP (which is conjectured to be Bayes-optimal in some settings), but obtained with a much lower complexity, as the proposed algorithm does not require a computationally expensive singular value decomposition.
Publishing Year
Date Published
2022-01-01
Proceedings Title
Proceedings of the 39th International Conference on Machine Learning
Publisher
ML Research Press
Acknowledgement
The authors would like to thank the anonymous reviewers for their helpful comments. KK and MM were partially supported by the 2019 Lopez-Loreta Prize.
Volume
162
Article Number
22
Conference
ICML: International Conference on Machine Learning
Conference Location
Baltimore, MD, United States
Conference Date
2022-07-17 – 2022-07-23
IST-REx-ID

Cite this

Venkataramanan R, Kögler K, Mondelli M. Estimation in rotationally invariant generalized linear models via approximate message passing. In: Proceedings of the 39th International Conference on Machine Learning. Vol 162. ML Research Press; 2022.
Venkataramanan, R., Kögler, K., & Mondelli, M. (2022). Estimation in rotationally invariant generalized linear models via approximate message passing. In Proceedings of the 39th International Conference on Machine Learning (Vol. 162). Baltimore, MD, United States: ML Research Press.
Venkataramanan, Ramji, Kevin Kögler, and Marco Mondelli. “Estimation in Rotationally Invariant Generalized Linear Models via Approximate Message Passing.” In Proceedings of the 39th International Conference on Machine Learning, Vol. 162. ML Research Press, 2022.
R. Venkataramanan, K. Kögler, and M. Mondelli, “Estimation in rotationally invariant generalized linear models via approximate message passing,” in Proceedings of the 39th International Conference on Machine Learning, Baltimore, MD, United States, 2022, vol. 162.
Venkataramanan R, Kögler K, Mondelli M. 2022. Estimation in rotationally invariant generalized linear models via approximate message passing. Proceedings of the 39th International Conference on Machine Learning. ICML: International Conference on Machine Learning vol. 162, 22.
Venkataramanan, Ramji, et al. “Estimation in Rotationally Invariant Generalized Linear Models via Approximate Message Passing.” Proceedings of the 39th International Conference on Machine Learning, vol. 162, 22, ML Research Press, 2022.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]
Main File(s)
Access Level
OA Open Access
Date Uploaded
2023-02-13
MD5 Checksum
67436eb0a660789514cdf9db79e84683


Export

Marked Publications

Open Data ISTA Research Explorer

Search this title in

Google Scholar