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Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning.
Brownian motion in a field of force and the diffusion model of chemical reactions
Hendrik Anthony Kramers · 1940
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Stochastic Processes
Joseph Leo Doob · 1953
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Problem complexity and method efficiency in optimization
David Yudin Arkadii Nemirovsky · 1983
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Recursive stochastic algorithms for global optimization in Rˆd
S. B. Gelfand and S. K. Mitter · 1990
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The mixing rate of Markov chains, an isoperimetric inequality, and computing the volume
László Lovász and Miklós Simonovits · 1990
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Sampling and integration of near log-concave functions
David Applegate and Ravi Kannan · 1991
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Computing the volume of convex bodies: a case where randomness provably helps
Martin Dyer and Alan Frieze · 1991
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Martin Dyer, Alan Frieze, and Ravi Kannan · 1991
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Claude JP Bélisle, H Edwin Romeijn, and Robert L Smith · 1993
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László Lovász and Miklós Simonovits · 1993
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Kerrie L Mengersen and Richard L Tweedie · 1996
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Gareth O Roberts and Richard L Tweedie · 1996
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Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms
Gareth O Roberts and Richard L Tweedie · 1996
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Random walks and an o*(n5) volume algorithm for convex bodies
Ravi Kannan, Laszlo Lovasz, and Miklos Simonovits · 1997
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Optimal scaling of discrete approximations to Langevin diffusions
Gareth O. Roberts and Jeffrey S. Rosenthal · 1997
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Hit-and-Run mixes fast
László Lovász · 1999
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Geometric ergodicity of Metropolis algorithms
Søren Fiig Jarner and Ernst Hansen · 2000
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An introduction to MCMC for machine learning
Christophe Andrieu, Nando De Freitas, Arnaud Doucet, and Michael I Jordan · 2003
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Hit-and-Run from a corner
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László Lovász and Santosh Vempala · 2006
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László Lovász and Santosh Vempala · 2007
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Recent progress and open problems in algorithmic convex geometry
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MCMC using Hamiltonian dynamics
Radford M Neal · 2011
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Nonasymptotic mixing of the MALA algorithm
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Optimal scaling and diffusion limits for the Langevin algorithm in high dimensions
Natesh S Pillai, Andrew M Stuart, and Alexandre H Thiéry · 2012
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