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Paper Detail

Paper IDG.3.4
Paper Title Macroscopic Analysis of Vector Approximate Message Passing in a Model Mismatch Setting
Authors Takashi Takahashi, Tokyo Institute of Technology, Japan; Yoshiyuki Kabashima, The University of Tokyo, Japan
Session G.3: Compressed Sensing
Presentation Lecture
Track Graphs, Games, Sparsity, and Signal Processing
Manuscript  Click here to download the manuscript
Virtual Presentation  Click here to watch in the Virtual Symposium
Abstract Vector approximate message passing (VAMP) is an efficient approximate inference algorithm used for generalized linear models. Although VAMP exhibits excellent performance, particularly when measurement matrices are sampled from rotationally invariant ensembles, existing convergence and performance analyses have been limited mostly to cases in which the correct posterior distribution is available. Here, we extend the analyses for cases in which the correct posterior distribution is not used in the inference stage. We derive state evolution equations, which macroscopically describe the dynamics of VAMP, and show that their fixed point is consistent with the replica symmetric solution obtained by the replica method of statistical mechanics. We also show that the fixed point of VAMP can exhibit a microscopic instability, the critical condition of which agrees with that for breaking the replica symmetry. The results of numerical experiments support our findings.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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