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Using Perturbed Underdamped Langevin Dynamics to Efficiently Sample from Probability Distributions.

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This study introduces novel Langevin samplers with perturbed dynamics, improving sampling efficiency by reducing variance. These methods maintain the original invariant measure for broader applicability.

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Area of Science:

  • Computational Statistics
  • Markov Chain Monte Carlo Methods

Background:

  • Standard underdamped Langevin dynamics are widely used for sampling.
  • Improving the efficiency and reducing the variance of these samplers is crucial for practical applications.

Purpose of the Study:

  • To introduce and analyze novel Langevin samplers based on perturbations of standard underdamped Langevin dynamics.
  • To demonstrate that these perturbed samplers can achieve improved properties, particularly reduced asymptotic variance.

Main Methods:

  • Developing perturbed Langevin dynamics that preserve the invariant measure of the original dynamics.
  • Conducting theoretical analysis for Gaussian target distributions.
  • Performing numerical experiments with non-Gaussian target measures to validate theoretical findings.

Main Results:

  • The proposed perturbed Langevin samplers exhibit reduced asymptotic variance compared to standard methods.
  • Theoretical analysis confirms the effectiveness for Gaussian distributions.
  • Numerical experiments validate performance on non-Gaussian distributions.

Conclusions:

  • The novel perturbed Langevin samplers offer enhanced efficiency for statistical sampling.
  • These methods provide a valuable alternative for MCMC applications requiring variance reduction.