论文标题
通过动态功能方法分析贝叶斯推论算法
Analysis of Bayesian Inference Algorithms by the Dynamical Functional Approach
论文作者
论文摘要
我们在学生教师方面分析了使用大型高斯潜在变量模型的大致推断的算法的动力学。为了建模潜在变量之间的非平凡依赖关系，我们假设从旋转不变合奏中绘制的随机协方差矩阵。对于完美的数据模型匹配的情况，从复制方法得出的静态顺序参数的知识使我们能够根据具有固定矩阵的矩阵 - 矢量乘法来获得有效的算法更新。使用动态功能方法，我们在单个节点的热力学极限中获得了一个精确的有效随机过程。从中，我们获得了收敛速率的闭合表达式。分析结果与模拟大型模型的模拟非常吻合。
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.
