Analysis of Random Sequential Message Passing Algorithms for Approximate Inference

Abstract

We analyze the dynamics of a random sequential message passing 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. Moreover, we consider a model mismatching setting, where the teacher model and the one used by the student may be different. By means of dynamical functional approach, we obtain exact dynamical mean-field equations characterizing the dynamics of the inference algorithm. We also derive a range of model parameters for which the sequential algorithm does not converge. The boundary of this parameter range coincides with the de Almeida Thouless (AT) stability condition of the replica symmetric ansatz for the static probabilistic model.

References in corpus (4)

• Expectation Propagation for approximate Bayesian inference
• Memory-free dynamics for the TAP equations of Ising models with arbitrary rotation invariant ensembles of random coupling matrices
• Approximate Message Passing algorithms for rotationally invariant matrices
• Exact solution to the random sequential dynamics of a message passing algorithm

Cited by in corpus (1)

• Linear Operator Approximate Message Passing (OpAMP)