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We study Hamiltonian Monte Carlo (HMC) for sampling from a strongly logconcave density proportional to $e^{-f}$ where $f:\mathbb{R}^d \to \mathbb{R}$ is $\mu$-strongly convex and $L$-smooth (the condition number is $\kappa = L/\mu$).
Sampling and integration of near log-concave functions
David Applegate and Ravi Kannan · 1991
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Fast Algorithms for Logconcave Functions: Sampling, Rounding, Integration and Optimization
László Lovász and Santosh S. Vempala · 2006
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Ricci curvature of Markov chains on metric spaces
Yann Ollivier · 2009
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Positive curvature and Hamiltonian Monte Carlo
Christof Seiler, Simon Rubinstein-Salzedo, and Susan Holmes · 2014
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Theoretical guarantees for approximate sampling from smooth and log-concave densities
Arnak S. Dalalyan · 2017
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Mixing of Hamiltonian Monte Carlo on strongly log-concave distributions 1: continuous dynamics
Oren Mangoubi and Aaron Smith · 2017
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Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis
Maxim Raginsky, Alexander Rakhlin, and Matus Telgarsky · 2017
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A Hitting Time Analysis of Stochastic Gradient Langevin Dynamics
Yuchen Zhang, Percy S. Liang, and Moses Charikar · 2017
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On the theory of variance reduction for stochastic gradient Monte Carlo
Niladri S. Chatterji, Nicolas Flammarion, Yi-An Ma, Peter L. Bartlett, and Michael I. Jordan · 2018
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Sharp convergence rates for Langevin dynamics in the nonconvex setting
Xiang Cheng, Niladri S. Chatterji, Yasin Abbasi-Yadkori, Peter L. Bartlett, and Michael I. Jordan · 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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On sampling from a log-concave density using kinetic Langevin diffusions
Arnak S. Dalalyan and Lionel Riou-Durand · 2018
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Convergence rate of Riemannian Hamiltonian Monte Carlo and faster polytope volume computation
Yin Tat Lee and Santosh S. Vempala · 2018
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Dimensionally tight bounds for second-order Hamiltonian Monte Carlo
Oren Mangoubi and Nisheeth Vishnoi · 2018
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Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem
Andre Wibisono · 2018
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User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient
Arnak S. Dalalyan and Avetik Karagulyan · 2019
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Is There an Analog of Nesterov Acceleration for MCMC?
Yi-An Ma, Niladri Chatterji, Xiang Cheng, Nicolas Flammarion, Peter Bartlett, and Michael I. Jordan · 2019
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Log-concave sampling: Metropolis-Hastings algorithms are fast!
Raaz Dwivedi, Yuansi Chen, Martin J. Wainwright, and Bin Yu · 2018
Cited alongside, same era.
Algorithmic Theory of ODEs and Sampling from Well-conditioned Logconcave Densities
Yin Tat Lee, Zhao Song, and Santosh S. Vempala · 2018
Cited alongside, same era.
Mixing of Hamiltonian Monte Carlo on strongly log-concave distributions 2: Numerical integrators
Oren Mangoubi and Aaron Smith · 2019
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Rapid Convergence of the Unadjusted Langevin Algorithm: Log-Sobolev Suffices
Santosh S. Vempala and Andre Wibisono · 2019
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