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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2505.18427 |
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| _version_ | 1866911228814688256 |
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| author | Cuin, James Carbone, Davide Akyildiz, O. Deniz |
| author_facet | Cuin, James Carbone, Davide Akyildiz, O. Deniz |
| contents | We utilise a sampler originating from nonequilibrium statistical mechanics, termed here Jarzynski-adjusted Langevin algorithm (JALA), to build statistical estimation methods in latent variable models. We achieve this by leveraging Jarzynski's equality and developing algorithms based on a weighted version of the unadjusted Langevin algorithm (ULA) with recursively updated weights. Adapting this for latent variable models, we develop a sequential Monte Carlo (SMC) method that provides the maximum marginal likelihood estimate of the parameters, termed JALA-EM. Under suitable regularity assumptions on the marginal likelihood, we provide a nonasymptotic analysis of the JALA-EM scheme implemented with stochastic gradient descent and show that it provably converges to the maximum marginal likelihood estimate. We demonstrate the performance of JALA-EM on a variety of latent variable models and show that it performs comparably to existing methods in terms of accuracy and computational efficiency. Importantly, the ability to recursively estimate marginal likelihoods - an uncommon feature among scalable methods - makes our approach particularly suited for model selection, which we validate through dedicated experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18427 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Latent Variable Models via Jarzynski-adjusted Langevin Algorithm Cuin, James Carbone, Davide Akyildiz, O. Deniz Computation Machine Learning We utilise a sampler originating from nonequilibrium statistical mechanics, termed here Jarzynski-adjusted Langevin algorithm (JALA), to build statistical estimation methods in latent variable models. We achieve this by leveraging Jarzynski's equality and developing algorithms based on a weighted version of the unadjusted Langevin algorithm (ULA) with recursively updated weights. Adapting this for latent variable models, we develop a sequential Monte Carlo (SMC) method that provides the maximum marginal likelihood estimate of the parameters, termed JALA-EM. Under suitable regularity assumptions on the marginal likelihood, we provide a nonasymptotic analysis of the JALA-EM scheme implemented with stochastic gradient descent and show that it provably converges to the maximum marginal likelihood estimate. We demonstrate the performance of JALA-EM on a variety of latent variable models and show that it performs comparably to existing methods in terms of accuracy and computational efficiency. Importantly, the ability to recursively estimate marginal likelihoods - an uncommon feature among scalable methods - makes our approach particularly suited for model selection, which we validate through dedicated experiments. |
| title | Learning Latent Variable Models via Jarzynski-adjusted Langevin Algorithm |
| topic | Computation Machine Learning |
| url | https://arxiv.org/abs/2505.18427 |