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We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional.
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Introductory Lectures on Convex Optimization: A Basic Course
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Gradient Flows: In Metric Spaces and in the Space of Probability Measures
A. Luigi, N. Gigli, and G. Savaré · 2008
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Hypocoercivity
C. Villani · 2009
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Optimal Transport: Old and New
C. Villani · 2009
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MCMC using Hamiltonian dynamics
R. M. Neal · 2010
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Riemann manifold Langevin and Hamiltonian Monte Carlo methods
M. Girolami and B. Calderhead · 2011
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Exponential convergence to equilibrium for kinetic Fokker-Planck equations
S. Calogero · 2012
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A differential equation for modeling Nesterov’s accelerated gradient method: Theory and insights
W. Su, S. Boyd, and E. Candes · 2014
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Extension of convex function
M. Yan · 2014
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A complete recipe for stochastic gradient MCMC
Y.-A Ma, T. Chen, and E. Fox · 2015
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Adaptive restart for accelerated gradient schemes
B. O’donoghue and E. Candès · 2015
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Sampling from strongly log-concave distributions with the Unadjusted Langevin Algorithm
A. Durmus and E. Moulines · 2016
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On the theory of variance reduction for stochastic gradient Monte Carlo
N. Chatterji, N. Flammarion, Y.-A. Ma, P. Bartlett, and M. Jordan · 2018
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Convergence of Langevin MCMC in KL-divergence
X. Cheng and P. L. Bartlett · 2018
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Sharp convergence rates for Langevin dynamics in the nonconvex setting
X. Cheng, N. S. Chatterji, Y. Abbasi-Yadkori, P. L. Bartlett, and M. I. Jordan · 2018
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Underdamped Langevin MCMC: A non-asymptotic analysis
X. Cheng, N. S. Chatterji, P. L. Bartlett, and M. I. Jordan · 2018
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On sampling from a log-concave density using kinetic Langevin diffusions
A. S. Dalalyan and L. Riou-Durand · 2018
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Adaptive thermostats for noisy gradient systems
B. Leimkuhler and X. Shang · 2016
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Stochastic gradient geodesic MCMC methods
C. Liu, J. Zhu, and Y. Song · 2016
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A function space HMC algorithm with second order Langevin diffusion limit
M. Ottobre, N. S. Pillai, F. J. Pinski, and A. M. Stuart · 2016
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A Lyapunov analysis of momentum methods in optimization
A. Wilson, B. Recht, and M. I. Jordan · 2016
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Theoretical guarantees for approximate sampling from smooth and log-concave densities
A. S. Dalalyan · 2017
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User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient
A. S. Dalalyan and A. G. Karagulyan · 2017
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R. Dwivedi, Y. Chen, M. J. Wainwright, and B. Yu · 2018
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Global non-convex optimization with discretized diffusions
M. A. Erdogdu, L. Mackey, and O. Shamir · 2018
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Irreversible samplers from jump and continuous Markov processes
Y.-A Ma, E. B. Fox, T. Chen, and L. Wu · 2018
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Dimensionally tight running time bounds for second-order Hamiltonian Monte Carlo
O. Mangoubi and N. K. Vishnoi · 2018
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A. Wibisono · 2018
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Direct Runge-Kutta discretization achieves acceleration
J. Zhang, A. Mokhtari, S. Sra, and A. Jadbabaie · 2018
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The Zig-Zag process and super-efficient sampling for Bayesian analysis of big data
J. Bierkens, P. Fearnhead, and G. Roberts · 2019
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Breaking reversibility accelerates Langevin dynamics for global non-convex optimization
X. Gao, M. Gurbuzbalaban, and L. Zhu · 2019
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Sampling can be faster than optimization
Y.-A. Ma, Y. Chen, C. Jin, N. Flammarion, and M. I. Jordan · 2019
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Acceleration via Symplectic Discretization of High-Resolution Differential Equations
B. Shi, S. S. Du, W. J. Su, and M. I. Jordan · 2019
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