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Vector approximate message passing (VAMP) is an efficient approximateinference algorithm used for generalized linear models. Although VAMP exhibitsexcellent performance, particularly when measurement matrices are sampled fromrotationally invariant ensembles, existing convergence and performance analyseshave been limited mostly to cases in which the correct posterior distributionis available. Here, we extend the analyses for cases in which the correctposterior distribution is not used in the inference stage. We derive stateevolution equations, which macroscopically describe the dynamics of VAMP, andshow that their fixed point is consistent with the replica symmetric solutionobtained by the replica method of statistical mechanics. We also show that thefixed point of VAMP can exhibit a microscopic instability, the criticalcondition of which agrees with that for breaking the replica symmetry. Theresults of numerical experiments support our findings.

Macroscopic Analysis of Vector Approximate Message Passing in a Model Mismatch Setting