Learning Latent Variable Models via Jarzynski-adjusted Langevin Algorithm

• URL: http://arxiv.org/abs/2505.18427v1
• Date: Fri, 23 May 2025 23:40:57 GMT
• Title: Learning Latent Variable Models via Jarzynski-adjusted Langevin Algorithm
• Authors: James Cuin, Davide Carbone, O. Deniz Akyildiz,
• Abstract summary: We utilise a sampler originating from nonequilibrium statistical mechanics to build estimation methods in latent variable models.<n>We develop a sequential Monte Carlo (SMC) method that provides the maximum marginal likelihood estimate of the parameters.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Variational Bayesian surrogate modelling with application to robust design optimisation [0.9626666671366836]
  Surrogate models provide a quick-to-evaluate approximation to complex computational models. We consider Bayesian inference for constructing statistical surrogates with input uncertainties and dimensionality reduction. We demonstrate intrinsic and robust structural optimisation problems where cost functions depend on a weighted sum of the mean and standard deviation of model outputs.
  arXiv  Detail & Related papers  (2024-04-23T09:22:35Z)
• Online Variational Sequential Monte Carlo [49.97673761305336]
  We build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference. Online VSMC is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation.
  arXiv  Detail & Related papers  (2023-12-19T21:45:38Z)
• Efficient Training of Energy-Based Models Using Jarzynski Equality [13.636994997309307]
  Energy-based models (EBMs) are generative models inspired by statistical physics. The computation of its gradient with respect to the model parameters requires sampling the model distribution. Here we show how results for nonequilibrium thermodynamics based on Jarzynski equality can be used to perform this computation efficiently.
  arXiv  Detail & Related papers  (2023-05-30T21:07:52Z)
• Numerically Stable Sparse Gaussian Processes via Minimum Separation using Cover Trees [57.67528738886731]
  We study the numerical stability of scalable sparse approximations based on inducing points. For low-dimensional tasks such as geospatial modeling, we propose an automated method for computing inducing points satisfying these conditions.
  arXiv  Detail & Related papers  (2022-10-14T15:20:17Z)
• Adaptive LASSO estimation for functional hidden dynamic geostatistical model [69.10717733870575]
  We propose a novel model selection algorithm based on a penalized maximum likelihood estimator (PMLE) for functional hiddenstatistical models (f-HD) The algorithm is based on iterative optimisation and uses an adaptive least absolute shrinkage and selector operator (GMSOLAS) penalty function, wherein the weights are obtained by the unpenalised f-HD maximum-likelihood estimators.
  arXiv  Detail & Related papers  (2022-08-10T19:17:45Z)
• Community Detection in the Stochastic Block Model by Mixed Integer Programming [3.8073142980733]
  Degree-Corrected Block Model (DCSBM) is a popular model to generate random graphs with community structure given an expected degree sequence. Standard approach of community detection based on the DCSBM is to search for the model parameters that are the most likely to have produced the observed network data through maximum likelihood estimation (MLE) We present mathematical programming formulations and exact solution methods that can provably find the model parameters and community assignments of maximum likelihood given an observed graph.
  arXiv  Detail & Related papers  (2021-01-26T22:04:40Z)
• Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
  We propose a novel compound kernel that captures the control-affine nature of the problem. We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
  arXiv  Detail & Related papers  (2020-11-14T01:27:32Z)
• Control as Hybrid Inference [62.997667081978825]
  We present an implementation of CHI which naturally mediates the balance between iterative and amortised inference. We verify the scalability of our algorithm on a continuous control benchmark, demonstrating that it outperforms strong model-free and model-based baselines.
  arXiv  Detail & Related papers  (2020-07-11T19:44:09Z)
• Joint Stochastic Approximation and Its Application to Learning Discrete Latent Variable Models [19.07718284287928]
  We show that the difficulty of obtaining reliable gradients for the inference model and the drawback of indirectly optimizing the target log-likelihood can be gracefully addressed. We propose to directly maximize the target log-likelihood and simultaneously minimize the inclusive divergence between the posterior and the inference model. The resulting learning algorithm is called joint SA (JSA)
  arXiv  Detail & Related papers  (2020-05-28T13:50:08Z)
• SUMO: Unbiased Estimation of Log Marginal Probability for Latent Variable Models [80.22609163316459]
  We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models based on randomized truncation of infinite series. We show that models trained using our estimator give better test-set likelihoods than a standard importance-sampling based approach for the same average computational cost.
  arXiv  Detail & Related papers  (2020-04-01T11:49:30Z)
• Efficient Debiased Evidence Estimation by Multilevel Monte Carlo Sampling [0.0]
  We propose a new optimization algorithm for Bayesian inference based multilevel Monte Carlo (MLMC) methods. Our numerical results confirm considerable computational savings compared to the conventional estimators.
  arXiv  Detail & Related papers  (2020-01-14T09:14:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.