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Algorithms based on discretizing Langevin diffusion are popular tools for sampling from high-dimensional distributions.
Exponential convergence of Langevin distributions and their discrete approximations
Roberts, G. O. and Tweedie, R. L. (1996) · 1996
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The variational formulation of the Fokker–Planck equation
Jordan, R., Kinderlehrer, D., and Otto, F. (1998) · 1998
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Geometric ergodicity of Metropolis algorithms
Jarner, S. F. and Hansen, E. (2000) · 2000
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Langevin diffusions and Metropolis-Hastings algorithms
Roberts, G. O. and Stramer, O. (2002) · 2002
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Gradient Flows in Metric Spaces and in the Space of Probability Measures
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Langevin diffusions and the Metropolis-adjusted Langevin algorithm
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Splitting Methods for Partial Differential Equations with Rough Solutions
Holden, H., Karlsen, K. H., Lie, K.-A., and Risebro, N. H. (2010) · 2010
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Regularized regression and density estimation based on optimal transport
Burger, M., Franek, M., and Schönlieb, C.-B. (2012) · 2012
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Optimal scaling and diffusion limits for the Langevin algorithm in high dimensions
Pillai, N. S., Stuart, A. M., and Thiéry, A. H. (2012) · 2012
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Introductory lectures on convex optimization: A basic course
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Theoretical guarantees for approximate sampling from smooth and log-concave densities
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Parikh, N. and Boyd, S. (2014) · 2014
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Durmus, A., Moulines, E., and Pereyra, M. (2016) · 2016
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Proximal Markov chain Monte Carlo algorithms
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{ \{ Euclidean, Metric, and Wasserstein } \} Gradient Flows: an overview
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Carrillo, J. A., Craig, K., and Patacchini, F. S. (2017) · 2017
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Convergence of Langevin MCMC in KL-divergence
Cheng, X. and Bartlett, P. (2017) · 2017
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Bowles, M. and Agueh, M. (2015) · 2015
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A finite-volume method for nonlinear nonlocal equations with a gradient flow structure
Carrillo, J. A., Chertock, A., and Huang, Y. (2015a)
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Dalalyan, A. S. (2017) · 2017
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User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient
Dalalyan, A. S. and Karagulyan, A. G. (2017) · 2017
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Nonasymptotic convergence analysis for the unadjusted Langevin algorithm
Durmus, A. and Moulines, E. (2017) · 2017
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Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces
Legendre, G. and Turinici, G. (2017) · 2017
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Model Averaging in Large Scale Learning
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A BDF2-approach for the non-linear Fokker-Planck equation
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