Particle algorithms for maximum likelihood training of latent variable models
This work provides a novel optimization approach for latent variable models, which is incremental as it builds on existing free energy methods.
The paper tackles the problem of maximum likelihood estimation in latent variable models by proposing particle-based algorithms derived from gradient flows of the free energy functional, achieving scalability to high-dimensional settings and good performance in numerical experiments.
(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.