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 in excellent agreement with simulations of single instances of large models.

中文翻译：

---

用动力学函数方法分析贝叶斯推理算法

我们在学生-教师场景中分析了使用大型高斯潜变量模型进行近似推理的算法的动力学。为了对潜在变量之间的非平凡依赖性进行建模，我们假设从旋转不变合奏中得出随机协方差矩阵。对于完美的数据模型匹配，从复制方法获得的静态顺序参数的知识使我们能够在固定矩阵的矩阵-矢量乘法方面获得有效的算法更新。使用动力学功能方法，我们在单个节点的热力学极限中获得了精确的有效随机过程。由此，我们获得收敛速度的闭式表达式。分析结果与大型模型的单个实例的仿真非常吻合。