Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics

• URL: http://arxiv.org/abs/2510.12311v1
• Date: Tue, 14 Oct 2025 09:10:37 GMT
• Title: Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics
• Authors: Joanna Marks, Tim Y. J. Wang, O. Deniz Akyildiz,
• Abstract summary: We develop interacting particle algorithms for learning latent variable models with energy-based priors.<n>Specifically, we provide a continuous-time framework for learning latent energy-based models, by defining a differential equations (SDEs)<n>We obtain a practical algorithm as a discretisation of these SDEs and provide theoretical guarantees for the convergence of the proposed algorithm.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop interacting particle algorithms for learning latent variable models with energy-based priors. To do so, we leverage recent developments in particle-based methods for solving maximum marginal likelihood estimation (MMLE) problems. Specifically, we provide a continuous-time framework for learning latent energy-based models, by defining stochastic differential equations (SDEs) that provably solve the MMLE problem. We obtain a practical algorithm as a discretisation of these SDEs and provide theoretical guarantees for the convergence of the proposed algorithm. Finally, we demonstrate the empirical effectiveness of our method on synthetic and image datasets.

Related papers

• Expanding the Chaos: Neural Operator for Stochastic (Partial) Differential Equations [65.80144621950981]
  We build on Wiener chaos expansions (WCE) to design neural operator (NO) architectures for SPDEs and SDEs.<n>We show that WCE-based neural operators provide a practical and scalable way to learn SDE/SPDE solution operators.
  arXiv  Detail & Related papers  (2026-01-03T00:59:25Z)
• A joint optimization approach to identifying sparse dynamics using least squares kernel collocation [70.13783231186183]
  We develop an all-at-once modeling framework for learning systems of ordinary differential equations (ODE) from scarce, partial, and noisy observations of the states.<n>The proposed methodology amounts to a combination of sparse recovery strategies for the ODE over a function library combined with techniques from reproducing kernel Hilbert space (RKHS) theory for estimating the state and discretizing the ODE.
  arXiv  Detail & Related papers  (2025-11-23T18:04:15Z)
• Equation discovery framework EPDE: Towards a better equation discovery [50.79602839359522]
  We enhance the EPDE algorithm -- an evolutionary optimization-based discovery framework.<n>Our approach generates terms using fundamental building blocks such as elementary functions and individual differentials.<n>We validate our algorithm's noise resilience and overall performance by comparing its results with those from the state-of-the-art equation discovery framework SINDy.
  arXiv  Detail & Related papers  (2024-12-28T15:58:44Z)
• Modeling AdaGrad, RMSProp, and Adam with Integro-Differential Equations [0.0]
  We propose a continuous-time formulation for the AdaGrad, RMSProp, and Adam optimization algorithms.<n>We perform numerical simulations of these equations, along with stability and convergence analyses, to demonstrate their validity as accurate approximations of the original algorithms.
  arXiv  Detail & Related papers  (2024-11-14T19:00:01Z)
• Proximal Interacting Particle Langevin Algorithms [0.0]
  PIPLA family can be the de facto choice for parameter estimation problems in non-differentiable latent variable models.<n>We show that PIPLA family can be the de facto choice for parameter estimation problems in non-differentiable latent variable models.
  arXiv  Detail & Related papers  (2024-06-20T13:16:41Z)
• CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problems [1.0923877073891446]
  This work extends the reach of generative models into physical problem domains. We present an efficient approach to promote consistency with the underlying PDE. We showcase the potential and versatility of score-based generative models in various physics tasks.
  arXiv  Detail & Related papers  (2023-12-16T19:56:10Z)
• Momentum Particle Maximum Likelihood [2.4561590439700076]
  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.
  arXiv  Detail & Related papers  (2023-12-12T14:53:18Z)
• Learning Space-Time Continuous Neural PDEs from Partially Observed States [13.01244901400942]
  We introduce a grid-independent model learning partial differential equations (PDEs) from noisy and partial observations on irregular grids. We propose a space-time continuous latent neural PDE model with an efficient probabilistic framework and a novel design encoder for improved data efficiency and grid independence.
  arXiv  Detail & Related papers  (2023-07-09T06:53:59Z)
• A Geometric Perspective on Diffusion Models [57.27857591493788]
  We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
  arXiv  Detail & Related papers  (2023-05-31T15:33:16Z)
• Latent Variable Representation for Reinforcement Learning [131.03944557979725]
  It remains unclear theoretically and empirically how latent variable models may facilitate learning, planning, and exploration to improve the sample efficiency of model-based reinforcement learning. We provide a representation view of the latent variable models for state-action value functions, which allows both tractable variational learning algorithm and effective implementation of the optimism/pessimism principle. In particular, we propose a computationally efficient planning algorithm with UCB exploration by incorporating kernel embeddings of latent variable models.
  arXiv  Detail & Related papers  (2022-12-17T00:26:31Z)
• Sampling with Mollified Interaction Energy Descent [57.00583139477843]
  We present a new optimization-based method for sampling called mollified interaction energy descent (MIED) MIED minimizes a new class of energies on probability measures called mollified interaction energies (MIEs) We show experimentally that for unconstrained sampling problems our algorithm performs on par with existing particle-based algorithms like SVGD.
  arXiv  Detail & Related papers  (2022-10-24T16:54:18Z)
• Mixed Effects Neural ODE: A Variational Approximation for Analyzing the Dynamics of Panel Data [50.23363975709122]
  We propose a probabilistic model called ME-NODE to incorporate (fixed + random) mixed effects for analyzing panel data. We show that our model can be derived using smooth approximations of SDEs provided by the Wong-Zakai theorem. We then derive Evidence Based Lower Bounds for ME-NODE, and develop (efficient) training algorithms.
  arXiv  Detail & Related papers  (2022-02-18T22:41:51Z)

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.