Neural Network Approach to Stochastic Dynamics for Smooth Multimodal Density Estimation

• URL: http://arxiv.org/abs/2503.17807v2
• Date: Fri, 28 Mar 2025 16:22:34 GMT
• Title: Neural Network Approach to Stochastic Dynamics for Smooth Multimodal Density Estimation
• Authors: Z. Zarezadeh, N. Zarezadeh,
• Abstract summary: We extent Metropolis-Adjusted Langevin Diffusion algorithm by modelling the Eigenity of precondition matrix as a random matrix.<n>The proposed method provides fully adaptation mechanisms to tune proposal densities to exploits and adapts the geometry of local structures of statistical models.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent Metropolis-Adjusted Langevin Diffusion algorithm by modelling the stochasticity of precondition matrix as a random matrix. An advantage compared to other proposal method is that it only requires the gradient of log-posterior. The proposed method provides fully adaptation mechanisms to tune proposal densities to exploits and adapts the geometry of local structures of statistical models. We clarify the benefits of the new proposal by modelling a Quantum Probability Density Functions of a free particle in a plane (energy Eigen-functions). The proposed model represents a remarkable improvement in terms of performance accuracy and computational time over standard MCMC method.

Related papers

• Multi-fidelity Parameter Estimation Using Conditional Diffusion Models [6.934199382834925]
  We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems. We use conditional generative models trained to sample the target conditional distribution. We demonstrate the effectiveness of the proposed method on several numerical examples.
  arXiv  Detail & Related papers  (2025-04-02T16:54:47Z)
• Dynamical Measure Transport and Neural PDE Solvers for Sampling [77.38204731939273]
  We tackle the task of sampling from a probability density as transporting a tractable density function to the target. We employ physics-informed neural networks (PINNs) to approximate the respective partial differential equations (PDEs) solutions. PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently.
  arXiv  Detail & Related papers  (2024-07-10T17:39:50Z)
• Proximal Interacting Particle Langevin Algorithms [0.0]
  We introduce Proximal Interacting Particle Langevin Algorithms (PIPLA) for inference and learning in latent variable models. We propose several variants within the novel proximal IPLA family, tailored to the problem of estimating parameters in a non-differentiable statistical model. Our theory and experiments together show that PIPLA family can be the de facto choice for parameter estimation problems in latent variable models for non-differentiable models.
  arXiv  Detail & Related papers  (2024-06-20T13:16:41Z)
• 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)
• Probabilistic Unrolling: Scalable, Inverse-Free Maximum Likelihood Estimation for Latent Gaussian Models [69.22568644711113]
  We introduce probabilistic unrolling, a method that combines Monte Carlo sampling with iterative linear solvers to circumvent matrix inversions. Our theoretical analyses reveal that unrolling and backpropagation through the iterations of the solver can accelerate gradient estimation for maximum likelihood estimation. In experiments on simulated and real data, we demonstrate that probabilistic unrolling learns latent Gaussian models up to an order of magnitude faster than gradient EM, with minimal losses in model performance.
  arXiv  Detail & Related papers  (2023-06-05T21:08:34Z)
• Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation [59.45669299295436]
  We propose a Monte Carlo PDE solver for training unsupervised neural solvers.<n>We use the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles.<n>Our experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency.
  arXiv  Detail & Related papers  (2023-02-10T08:05:19Z)
• Gaussian process regression and conditional Karhunen-Lo\'{e}ve models for data assimilation in inverse problems [68.8204255655161]
  We present a model inversion algorithm, CKLEMAP, for data assimilation and parameter estimation in partial differential equation models. The CKLEMAP method provides better scalability compared to the standard MAP method.
  arXiv  Detail & Related papers  (2023-01-26T18:14:12Z)
• Scalable Stochastic Parametric Verification with Stochastic Variational Smoothed Model Checking [1.5293427903448025]
  Smoothed model checking (smMC) aims at inferring the satisfaction function over the entire parameter space from a limited set of observations. In this paper, we exploit recent advances in probabilistic machine learning to push this limitation forward. We compare the performances of smMC against those of SV-smMC by looking at the scalability, the computational efficiency and the accuracy of the reconstructed satisfaction function.
  arXiv  Detail & Related papers  (2022-05-11T10:43:23Z)
• Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC [83.48593305367523]
  Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo method for sampling from complex continuous distributions. We introduce a new approach based on augmenting Monte Carlo methods with SurVAE Flows to sample from discrete distributions. We demonstrate the efficacy of our algorithm on a range of examples from statistics, computational physics and machine learning, and observe improvements compared to alternative algorithms.
  arXiv  Detail & Related papers  (2021-02-04T02:21:08Z)
• Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes [3.564709604457361]
  "Projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to be inferred jointly with the GP parameters. We extend the proposed framework to multi-fidelity models using GPs including the scenarios of training multiple outputs together. The benefits of our proposed framework, are illustrated on the computationally challenging three-dimensional aerodynamic optimization of a last-stage blade for an industrial gas turbine.
  arXiv  Detail & Related papers  (2020-08-05T22:28:53Z)
• Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
  We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
  arXiv  Detail & Related papers  (2020-07-16T13:27:47Z)

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.