2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | G.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. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
