Momentum Particle Maximum Likelihood

• URL: http://arxiv.org/abs/2312.07335v3
• Date: Tue, 4 Jun 2024 17:17:53 GMT
• Title: Momentum Particle Maximum Likelihood
• Authors: Jen Ning Lim, Juan Kuntz, Samuel Power, Adam M. Johansen,
• Abstract summary: We propose an analogous dynamical-systems-inspired approach to minimizing the free energy functional. By discretizing the system, we obtain a practical algorithm for Maximum likelihood estimation in latent variable models. The algorithm outperforms existing particle methods in numerical experiments and compares favourably with other MLE algorithms.
• Score: 2.4561590439700076
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with insights from optimal transport to obtain novel particle-based algorithms for fitting latent variable models to data. Drawing inspiration from prior works which interpret `momentum-enriched' optimization algorithms as discretizations of ordinary differential equations, we propose an analogous dynamical-systems-inspired approach to minimizing the free energy functional. The result is a dynamical system that blends elements of Nesterov's Accelerated Gradient method, the underdamped Langevin diffusion, and particle methods. Under suitable assumptions, we prove that the continuous-time system minimizes the functional. By discretizing the system, we obtain a practical algorithm for MLE in latent variable models. The algorithm outperforms existing particle methods in numerical experiments and compares favourably with other MLE algorithms.

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