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We give the first rigorous proof of the convergence of Riemannian Hamiltonian Monte Carlo, a general (and practical) method for sampling Gibbs distributions.
A random polynomial time algorithm for approximating the volume of convex bodies
M. E. Dyer, A. M. Frieze, and R. Kannan · 1989
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Mixing rate of Markov chains, an isoperimetric inequality, and computing the volume
L. Lovász and M. Simonovits · 1990
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Sampling and integration of near log-concave functions
D. Applegate and R. Kannan · 1991
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Computing the volume of a convex body: a case where randomness provably helps
M. E. Dyer and A. M. Frieze · 1991
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On the randomized complexity of volume and diameter
L. Lovász and M. Simonovits · 1992
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Random walks in a convex body and an improved volume algorithm
L. Lovász and M. Simonovits · 1993
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Interior-point polynomial algorithms in convex programming
Yurii Nesterov, Arkadii Nemirovskii, and Yinyu Ye · 1994
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Isoperimetric problems for convex bodies and a localization lemma
R. Kannan, L. Lovász, and M. Simonovits · 1995
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Bayesian Learning for Neural Networks
R.M. Neal · 1996
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Random walks and an O ∗ ( n 5 ) O^{*}(n^{5}) volume algorithm for convex bodies
R. Kannan, L. Lovász, and M. Simonovits · 1997
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The curvature of a hessian metric
Burt Totaro · 2004
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Geometric random walks: A survey
S. Vempala · 2005
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Simulated annealing for convex optimization
A. T. Kalai and S. Vempala · 2006
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Fast algorithms for logconcave functions: sampling, rounding, integration and optimization
L. Lovász and S. Vempala · 2006
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Hit-and-run from a corner
L. Lovász and S. Vempala · 2006
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Simulated annealing in convex bodies and an O ∗ ( n 4 ) O^{*}(n^{4}) volume algorithm
L. Lovász and S. Vempala · 2006
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The geometry of logconcave functions and sampling algorithms
Riemann manifold langevin and hamiltonian monte carlo methods
Mark Girolami and Ben Calderhead · 2011
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Path finding methods for linear programming: Solving linear programs in õ (vrank) iterations and faster algorithms for maximum flow
Yin Tat Lee and Aaron Sidford · 2014
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Bypassing KLS: Gaussian cooling and an O ∗ ( n 3 ) O^{*}(n^{3}) volume algorithm
B. Cousins and S. Vempala · 2015
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Yin Tat Lee and Santosh S. Vempala · 2016
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Yin Tat Lee and Santosh Srinivas Vempala · 2016
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L. Lovász and S. Vempala · 2007
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Riemannian Manifold Hamiltonian Monte Carlo
M. Girolami, B. Calderhead, and S. A. Chin · 2009
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Random walks on polytopes and an affine interior point method for linear programming
R. Kannan and H. Narayanan · 2009
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MCMC using Hamiltonian dynamics
Radford M. Neal · 2010
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A Conceptual Introduction to Hamiltonian Monte Carlo
M. Betancourt · 2017
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Eldan’s stochastic localization and the KLS hyperplane conjecture: An improved lower bound for expansion
Yin Tat Lee and Santosh Srinivas Vempala · 2017
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Geodesic walks in polytopes
Yin Tat Lee and Santosh Srinivas Vempala · 2017
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Rapid mixing of hamiltonian monte carlo on strongly log-concave distributions
Oren Mangoubi and Aaron Smith · 2017
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