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We analyze the dynamics of a random sequential message passing algorithm forapproximate inference with large Gaussian latent variable models in astudent-teacher scenario. To model nontrivial dependencies between the latentvariables, we assume random covariance matrices drawn from rotation invariantensembles. Moreover, we consider a model mismatching setting, where the teachermodel and the one used by the student may be different. By means of dynamicalfunctional approach, we obtain exact dynamical mean-field equationscharacterizing the dynamics of the inference algorithm. We also derive a rangeof model parameters for which the sequential algorithm does not converge. Theboundary of this parameter range coincides with the de Almeida Thouless (AT)stability condition of the replica symmetric ansatz for the staticprobabilistic model.

Analysis of Random Sequential Message Passing Algorithms for Approximate Inference