scholarly journals Langevin diffusions and the Metropolis-adjusted Langevin algorithm

2014 ◽  
Vol 91 ◽  
pp. 14-19 ◽  
Author(s):  
T. Xifara ◽  
C. Sherlock ◽  
S. Livingstone ◽  
S. Byrne ◽  
M. Girolami
Keyword(s):  
Langevin Diffusions

scholarly journals Interacting Langevin Diffusions: Gradient Structure and Ensemble Kalman Sampler

2020 ◽  
Vol 19 (1) ◽  
pp. 412-441 ◽  
Author(s):  
Alfredo Garbuno-Inigo ◽  
Franca Hoffmann ◽  
Wuchen Li ◽  
Andrew M. Stuart
Keyword(s):  
Gradient Structure ◽  
Langevin Diffusions

scholarly journals Langevin diffusions on the torus: estimation and applications

2017 ◽  
Vol 29 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Eduardo García-Portugués ◽  
Michael Sørensen ◽  
Kanti V. Mardia ◽  
Thomas Hamelryck
Keyword(s):  
Langevin Diffusions

scholarly journals On sampling from a log-concave density using kinetic Langevin diffusions

Bernoulli ◽  
2020 ◽  
Vol 26 (3) ◽  
pp. 1956-1988
Author(s):  
Arnak S. Dalalyan ◽  
Lionel Riou-Durand
Keyword(s):  
Langevin Diffusions

scholarly journals Dynamical Sampling with Langevin Normalization Flows

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1096 ◽  
Author(s):  
Minghao Gu ◽  
Shiliang Sun ◽  
Yan Liu
Keyword(s):  
Monte Carlo ◽  
Sampling Method ◽  
Sampling Methods ◽  
Probability Distributions ◽  
Unbiased Estimation ◽  
Rapid Convergence ◽  
Target Distribution ◽  
Leibler Divergence ◽  
Langevin Diffusions ◽  
Bayesian Machine Learning

In Bayesian machine learning, sampling methods provide the asymptotically unbiased estimation for the inference of the complex probability distributions, where Markov chain Monte Carlo (MCMC) is one of the most popular sampling methods. However, MCMC can lead to high autocorrelation of samples or poor performances in some complex distributions. In this paper, we introduce Langevin diffusions to normalization flows to construct a brand-new dynamical sampling method. We propose the modified Kullback-Leibler divergence as the loss function to train the sampler, which ensures that the samples generated from the proposed method can converge to the target distribution. Since the gradient function of the target distribution is used during the process of calculating the modified Kullback-Leibler, which makes the integral of the modified Kullback-Leibler intractable. We utilize the Monte Carlo estimator to approximate this integral. We also discuss the situation when the target distribution is unnormalized. We illustrate the properties and performances of the proposed method on varieties of complex distributions and real datasets. The experiments indicate that the proposed method not only takes the advantage of the flexibility of neural networks but also utilizes the property of rapid convergence to the target distribution of the dynamics system and demonstrate superior performances competing with dynamics based MCMC samplers.

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