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We extend the Langevin Monte Carlo (LMC) algorithm to compactly supported measures via a projection step, akin to projected Stochastic Gradient Descent (SGD).
A stochastic approximation method
H. Robbins and S. Monro · 1951
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Stochastic equations for diffusion processes in a bounded region
A. Skorokhod · 1961
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Stochastic differential equations with reflecting boundary condition in convex regions
H. Tanaka · 1979
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Problem Complexity and Method Efficiency in Optimization
A. Nemirovski and D. Yudin · 1983
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Stochastic minimization with constant step-size: asymptotic laws
G. Pflug · 1986
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A random polynomial-time algorithm for approximating the volume of convex bodies
M. Dyer, A. Frieze, and R. Kannan · 1991
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Exponential convergence of langevin distributions and their discrete approximations
L. Tweedie and G. Roberts · 1996
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Hit-and-run from a corner
L. Lovász and S. Vempala · 2006
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The geometry of logconcave functions and sampling algorithms
L. Lovász and S. Vempala · 2007
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Markov Chains and Mixing Times
David A. Levin, Yuval Peres, and Elizabeth L. Wilmer · 2008
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Bayesian learning via stochastic gradient langevin dynamics
M. Welling and Y.W. Teh · 2011
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Bayesian posterior sampling via stochastic gradient fisher scoring
S. Ahn, A. Korattikara, and M. Welling · 2012
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Random walks on polytopes and an affine interior point method for linear programming
R. Kannan and H. Narayanan · 2012
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Non-strongly-convex smooth stochastic approximation with convergence rate o(1/n)
F. Bach and E. Moulines · 2013
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Representation formula for the entropy and functional inequalities
J. Lehec · 2013
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Bypassing kls: Gaussian cooling and an o ∗ ( n 3 ) o^{*}(n^{3}) volume algorithm
B. Cousins and S. Vempala · 2014
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Theoretical guarantees for approximate sampling from smooth and log-concave densities
A. Dalalyan · 2014
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