  We analyze the dynamics of an algorithm for approximate inference with large
Gaussian latent variable models in a student-teacher scenario. To model
nontrivial dependencies between the latent variables, we assume random
covariance matrices drawn from rotation invariant ensembles. For the case of
perfect data-model matching, the knowledge of static order parameters derived
from the replica method allows us to obtain efficient algorithmic updates in
terms of matrix-vector multiplications with a fixed matrix. Using the dynamical
functional approach, we obtain an exact effective stochastic process in the
thermodynamic limit for a single node. From this, we obtain closed-form
expressions for the rate of the convergence. Analytical results are excellent
agreement with simulations of single instances of large models.
