论文标题
坐标上升变化推断的动力学：2D ISING模型中的案例研究
Dynamics of coordinate ascent variational inference: A case study in 2D Ising models
论文作者
论文摘要
在过去的二十年中，变异算法已成为贝叶斯推断的可扩展计算环境。在本文中，我们探讨了从动力学系统文献中的工具来研究平均场变异推理的坐标上升算法的收敛性。专注于在两个节点上定义的ISING模型，我们充分表征了顺序坐标上升算法及其并行版本的动力学。我们观察到，在目标函数为凸的机制中，两种算法都是稳定的，并且表现出与唯一固定点的收敛。我们的分析揭示了当目标函数是非convex时，该区域的这两个版本之间的有趣{\ em Discordances}。实际上，并行版本表现出一种周期性的振荡行为，在顺序版本中不存在。从马尔可夫链蒙特卡洛文学中绘制直觉，我们{\ em从经验上}表明，伊辛模型的参数扩展通常被称为爱德华 - 俄罗斯耦合，导致了收敛性与全局优点的融合方面的扩大。
Variational algorithms have gained prominence over the past two decades as a scalable computational environment for Bayesian inference. In this article, we explore tools from the dynamical systems literature to study convergence of coordinate ascent algorithms for mean field variational inference. Focusing on the Ising model defined on two nodes, we fully characterize the dynamics of the sequential coordinate ascent algorithm and its parallel version. We observe that in the regime where the objective function is convex, both the algorithms are stable and exhibit convergence to the unique fixed point. Our analyses reveal interesting {\em discordances} between these two versions of the algorithm in the region when the objective function is non-convex. In fact, the parallel version exhibits a periodic oscillatory behavior which is absent in the sequential version. Drawing intuition from the Markov chain Monte Carlo literature, we {\em empirically} show that a parameter expansion of the Ising model, popularly called as the Edward--Sokal coupling, leads to an enlargement of the regime of convergence to the global optima.
