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.
翻译:我们分析随机顺序电文传递算法的动态,以在学生-教师情景中与大型高斯潜伏变量模型进行近似推算。为了在潜伏变量之间建模非边际依赖性,我们假设从轮用变量组合中抽取随机共变矩阵。此外,我们考虑一个模型不匹配的设置,教师模型和学生使用的模型可能不同。通过动态功能方法,我们获得了精确的动态平均场方程式,这些方程式体现了推算算法的动态。我们还得出了一系列模型参数,而序列算法却无法汇合这些参数。这一参数范围的边界与静态概率模型的重复对称 ansatz 稳定性条件相吻合。