Analysis of random sequential message passing algorithms for approximate inference

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT(2022)

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摘要
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.
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关键词
analysis of algorithms, machine learning, message-passing algorithms, statistical inference
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