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Variance Reduction Using Nonreversible Langevin Samplers
A B Duncan1, T Lelièvre2, G A Pavliotis1
1Department of Mathematics, South Kensington Campus, Imperial College London, London, SW7 2AZ England.
Journal of Statistical Physics
|July 26, 2016
Summary
Adding nonreversible components to Langevin dynamics improves computational efficiency for target distributions. This study details how deviations from reversibility impact asymptotic variance, offering insights for faster convergence.
Area of Science:
- Computational statistics
- Stochastic processes
- Numerical analysis
Background:
- Standard methods for computing expectations use reversible overdamped Langevin equations.
- Recent research suggests nonreversible dynamics can accelerate convergence and reduce variance.
Purpose of the Study:
- To investigate the relationship between deviation from reversibility and asymptotic variance in Langevin dynamics.
- To provide a theoretical framework for understanding the benefits of nonreversible components.
Main Methods:
- Analysis of overdamped Langevin equations with nonreversible components.
- Theoretical study of asymptotic variance dependence on reversibility.
- Numerical simulations to validate theoretical findings.
Main Results:
- Quantified the impact of nonreversible dynamics on asymptotic variance reduction.
- Demonstrated that controlled deviation from reversibility enhances convergence speed.
- Theoretical predictions were confirmed by simulation results.
Conclusions:
- Nonreversible Langevin dynamics offer significant advantages over standard reversible methods.
- Understanding the precise dependence on reversibility is key to optimizing computational efficiency.
- This work provides a foundation for developing more effective sampling algorithms.
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