(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional $F$, and the EM algorithm as coordinate descent applied to $F$. Here, we explore alternative ways to optimize the functional. In particular, we identify various gradient flows associated with $F$ and show that their limits coincide with $F$'s stationary points. By discretizing the flows, we obtain practical particle-based algorithms for maximum likelihood estimation in broad classes of latent variable models. The novel algorithms scale to high-dimensional settings and perform well in numerical experiments.

翻译：(Neal和Hinton, 1998)将任意给定潜变量模型的最大似然估计重新表述为自由能函数$F$的最小化，并将EM算法视为对$F$施加的坐标下降法。本文探索了优化该函数的替代方法.具体而言,我们识别了与$F$相关的各种梯度流,并证明了这些梯度流的极限与$F$的驻点一致。通过对这些流进行离散化,我们获得了适用于广泛类别潜变量模型最大似然估计的实用粒子算法。这些新颖算法可扩展至高维场景,并在数值实验中表现优异。