Analysis of Bayesian inference algorithms by the dynamical functional approach
Analysis of Bayesian inference algorithms by the dynamical functional approach
复制标题
通过动态泛函方法分析贝叶斯推理算法
DOI：
10.1088/1751-8121/ab8ff4
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
M. Opper
中科院分区：
文献类型：
--
作者：
Burak Çakmak;M. Opper
我们分析了一个算法的动态近似推理与大高斯潜变量模型在学生-教师的情况。为了对潜在变量之间的非平凡依赖关系进行建模，我们假设从旋转不变集合中提取随机协方差矩阵。对于完美的数据模型匹配的情况下，来自副本方法的静态顺序参数的知识，使我们能够获得有效的算法更新的矩阵向量乘法与一个固定的矩阵。利用动力泛函方法，我们得到了一个精确的有效随机过程的热力学极限为一个单一的节点。由此，我们得到了收敛速度的封闭形式表达式。分析结果与大型模型的单个实例的模拟非常一致。
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.