High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithm
Authors: Wenlong Mou, Yi-An Ma, Martin J. Wainwright, Peter L. Bartlett, Michael I. Jordan
JMLR 2021 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We propose a Markov chain Monte Carlo (MCMC) algorithm based on third-order Langevin dynamics for sampling from distributions with smooth, log-concave densities. The higher-order dynamics allow for more flexible discretization schemes, and we develop a specific method that combines splitting with more accurate integration. For a broad class of d-dimensional distributions arising from generalized linear models, we prove that the resulting third-order algorithm produces samples from a distribution that is at most ε > 0 in Wasserstein distance from the target distribution in O d1/4 ε1/2 steps. |
| Researcher Affiliation | Academia | Wenlong Mou EMAIL Department of EECS University of California, Berkeley Berkeley, CA, 94720, USA Yi-An Ma EMAIL Halicio glu Data Science Institute University of California, San Diego La Jolla, CA 92023, USA Martin J. Wainwright EMAIL Department of EECS and Department of Statistics University of California, Berkeley Berkeley, CA, 94720, USA Peter L. Bartlett EMAIL Department of EECS and Department of Statistics University of California, Berkeley Berkeley, CA, 94720, USA Michael I. Jordan EMAIL Department of EECS and Department of Statistics University of California, Berkeley Berkeley, CA, 94720, USA |
| Pseudocode | Yes | Algorithm 1: Discretized Third-Order Langevin Algorithm Let x(0) = (θ(0), p(0), r(0)) = (θ , 0, 0). for k = 0, , N 1 do Sample x(k+1) N µ x(k) , Σ , where µ and Σ are defined in (9a) and (9b). end for |
| Open Source Code | No | The paper does not contain any explicit statements about the availability of source code, nor does it provide links to any code repositories. The license information provided is for the paper itself, not for associated code. |
| Open Datasets | No | This paper is theoretical in nature and focuses on the mathematical analysis of an MCMC algorithm. It does not conduct empirical studies that would involve specific datasets, therefore, no information about open or public datasets is provided. |
| Dataset Splits | No | This paper is theoretical in nature and focuses on the mathematical analysis of an MCMC algorithm. It does not conduct empirical studies that would involve specific datasets or their splits. |
| Hardware Specification | No | This paper is theoretical in nature, focusing on the mathematical analysis and development of an MCMC algorithm. It does not describe any experimental implementations or empirical evaluations that would require specific hardware specifications. |
| Software Dependencies | No | This paper is theoretical in nature, focusing on the mathematical analysis and development of an MCMC algorithm. It does not describe any experimental implementations or empirical evaluations that would require specific software dependencies or version numbers. |
| Experiment Setup | No | This paper is theoretical, presenting an algorithm and its convergence properties without describing any practical implementation or empirical experimental results. Therefore, it does not include details such as hyperparameters, training configurations, or other system-level settings for experiments. |