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We study sampling as optimization in the space of measures.
Some inequalities satisfied by the quantities of information of Fisher and Shannon
A. J. Stam · 1959
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A well posed problem for the backward heat equation
Willard L. Miranker · 1961
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Une propriété topologique des sous-ensembles analytiques réels
Stanislaw Lojasiewicz · 1963
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Gradient methods for minimizing functionals
Boris T. Polyak · 1963
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Logarithmic Sobolev inequalities
Leonard Gross · 1975
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Logarithmic Sobolev inequalities and stochastic Ising models
Richard Holley and Daniel Stroock · 1987
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Information theoretic inequalities
Amir Dembo, Thomas M. Cover, and Joy A. Thomas · 1991
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Time’s Arrow: The Origins of Thermodynamics Behavior
Michael C. Mackey · 1992
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Exponential convergence of Langevin distributions and their discrete approximations
Gareth O. Roberts and Richard L. Tweedie · 1996
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Transportation cost for Gaussian and other product measures
Michel Talagrand · 1996
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Subgradient algorithm on Riemannian manifolds
O.P. Ferreira and P.R. Oliveira · 1998
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The variational formulation of the Fokker–Planck equation
Richard Jordan, David Kinderlehrer, and Felix Otto · 1998
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Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
Felix Otto and Cédric Villani · 2000
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A short proof of the ”concavity of entropy power”
Cédric Villani · 2000
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Proximal point algorithm on Riemannian manifolds
O.P. Ferreira and P.R. Oliveira · 2002
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Constrained steepest descent in the 2-Wasserstein metric
Eric A. Carlen and Wilfrid Gangbo · 2003
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Topics in optimal transportation
Cédric Villani · 2003
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Introductory Lectures on Convex Optimization: A Basic Course
Yurii Nesterov · 2004
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High-dimensional Bayesian inference via the unadjusted Langevin algorithm
Alain Durmus and Eric Moulines · 2016
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Linear convergence of gradient and proximal-gradient methods under the Polyak-Lojasiewicz condition
Hamed Karimi, Julie Nutini, and Mark Schmidt · 2016
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A variational perspective on accelerated methods in optimization
Andre Wibisono, Ashia C. Wilson, and Michael I. Jordan · 2016
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First-order methods for geodesically convex optimization
Hongyi Zhang and Suvrit Sra · 2016
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Further and stronger analogy between sampling and optimization: Langevin Monte Carlo and gradient descent
Arnak S. Dalalyan · 2017
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Proximal subgradient and a characterization of Lipschitz function on Riemannian manifolds
O.P. Ferreira · 2006
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Geometric numerical integration: Structure-preserving algorithms for ordinary differential equations , volume 31
Ernst Hairer, Christian Lubich, and Gerhard Wanner · 2006
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Gradient flows in metric spaces and in the space of probability measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2008
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Optimal Transport: Old and New , volume 338 of Grundlehren der mathematischen Wissenschaften
Cédric Villani · 2008
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Wasserstein geometry of Gaussian measures
Asuka Takatsu · 2011
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A new approach to the proximal point method: Convergence on general Riemannian manifolds
Glaydston de Carvalho Bento, João Xavier da Cruz Neto, and Paulo Roberto Oliveira · 2016
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Arnak S. Dalalyan and Avetik G. Karagulyan · 2017
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Convergence of the forward-backward algorithm: Beyond the worst case with the help of geometry
Guillaume Garrigos, Lorenzo Rosasco, and Silvia Villa · 2017
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Langevin Monte Carlo and JKO splitting
Espen Bernton · 2018
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Convergence of Langevin MCMC in KL-divergence
Xiang Cheng and Peter Bartlett · 2018
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Underdamped Langevin MCMC: A non-asymptotic analysis
Xiang Cheng, Niladri S. Chatterji, Peter L. Bartlett, and Michael I. Jordan · 2018
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Log-concave sampling: Metropolis-Hastings algorithms are fast!
Raaz Dwivedi, Yuansi Chen, Martin J. Wainwright, and Bin Yu · 2018
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