1. Rigorous State Evolution Analysis for Approximate Message Passing With Side Information
- Author
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Hangjin Liu, Cynthia Rush, and Dror Baron
- Subjects
Signal Processing (eess.SP) ,FOS: Computer and information sciences ,Statistics - Machine Learning ,FOS: Electrical engineering, electronic engineering, information engineering ,Machine Learning (stat.ML) ,Electrical Engineering and Systems Science - Signal Processing ,Library and Information Sciences ,Computer Science Applications ,Information Systems - Abstract
A common goal in many research areas is to reconstruct an unknown signal x from noisy linear measurements. Approximate message passing (AMP) is a class of low-complexity algorithms that can be used for efficiently solving such high-dimensional regression tasks. Often, it is the case that side information (SI) is available during reconstruction. For this reason, a novel algorithmic framework that incorporates SI into AMP, referred to as approximate message passing with side information (AMP-SI), has been recently introduced. In this work, we provide rigorous performance guarantees for AMP-SI when there are statistical dependencies between the signal and SI pairs and the entries of the measurement matrix are independent and identically distributed Gaussian. The AMP-SI performance is shown to be provably tracked by a scalar iteration referred to as state evolution. Moreover, we provide numerical examples that demonstrate empirically that the SE can predict the AMP-SI mean square error accurately., arXiv admin note: text overlap with arXiv:1902.00150
- Published
- 2023
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