Scalable particle-based alternatives to EM

(Neal and Hinton, 1998) recast the problem tackled by EM as the minimization of a free energy functional $F$ on an infinite-dimensional space and EM itself 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 three practical particle-based algorithms for maximum likelihood estimation in broad classes of latent variable models. The novel algorithms scale well to high-dimensional settings and outperform existing state-of-the-art methods in experiments.