Reproduce “Particle algorithms for maximum likelihood training of latent variable models” on OpenResearch

About this paper

Juan Kuntz, Jen Ning Lim, Adam M. Johansen

Kuntz, Lim, and Johansen introduce particle-based algorithms for maximum likelihood training of latent variable models by reframing the problem as a joint optimization of a free energy functional over model parameters and probability distributions. Their methods, Particle Gradient Descent (PGD), Particle Quasi-Newton (PQN), and Particle Marginal Gradient Descent (PMGD), exhibit faster computation and superior predictive performance compared to Monte Carlo EM variants across various models, including deep generative networks and Bayesian neural networks.

Key insights

• Reframing MLE as a joint gradient flow on a combined parameter and distribution space offers a flexible, non-alternating optimization approach beyond traditional EM algorithms.
• Leveraging Wasserstein-2 geometry provides a principled way to define gradients and optimize directly on the space of probability measures, enabling more accurate posterior approximations without restrictive parametric assumptions.
• Particle approximations based on unadjusted Langevin dynamics allow for scalable and efficient numerical solutions to these gradient flows, making them suitable for high-dimensional and complex latent variable models.

Summary by alphaXiv.