Momentum Particle Maximum Likelihood
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913376591937536 |
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| author | Lim, Jen Ning Kuntz, Juan Power, Samuel Johansen, Adam M. |
| author_facet | Lim, Jen Ning Kuntz, Juan Power, Samuel Johansen, Adam M. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_07335 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Momentum Particle Maximum Likelihood Lim, Jen Ning Kuntz, Juan Power, Samuel Johansen, Adam M. Machine Learning 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. |
| title | Momentum Particle Maximum Likelihood |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2312.07335 |