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Hamiltonian Monte Carlo (HMC) is a popular Markov chain Monte Carlo (MCMC) algorithm that generates proposals for a Metropolis-Hastings algorithm by simulating the dynamics of a Hamiltonian system.
On the Electrodynamics of Moving Bodies
A. Einstein · 1905
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Diffusions for global optimization
S. Geman and C. Hwang · 1986
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Hybrid Monte Carlo
S. Duane, A.D. Kennedy, B.J. Pendleton, and D. Roweth · 1987
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Numerical Hamiltonian problems
J. M. Sanz-Serna and M.P. Calvo · 1994
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Exponential convergence of langevin distributions and their discrete approximations
G. O. Roberts and R. L. Tweedie · 1996
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Adaptive Proposal Distribution for Random Walk Metropolis Algorithm
H. Haario, E. Saksman, and J. Tamminen · 1999
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Simulated annealing for maximum a posteriori parameter estimation of hidden Markov models
C. Andrieu and A. Doucet · 2000
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Statistical Thermodynamics: Fundamentals and Applications
Normand M Laurendeau · 2005
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Hypocoercivity
C. Villani · 2009
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A Metropolis adjusted Nosé-Hoover thermostat
B. Leimkuhler and S. Reich · 2009
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MCMC using Hamiltonian dynamics
R. M. Neal · 2010
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Bayesian Learning via Stochastic Gradient Langevin Dynamics
M. Welling and Y.W. Teh · 2011
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Riemann manifold Langevin and Hamiltonian Monte Carlo methods
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Adaptive Subgradient Methods for Online Learning and Stochastic Optimization
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Lecture 6.5-RMSProp: Divide the gradient by a running average of its recent magnitude, 2012
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Optimal tuning of hybrid Monte Carlo algorithm
A. Beskos, N. Pillai, G. O. Roberts, J. M. Sanz-Serna, and A. M. Stuart · 2013
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Stochastic Gradient Riemannian Langevin Dynamics on the Probability Simplex
S. Patterson and Y. W. Teh · 2013
A Complete Recipe for Stochastic Gradient MCMC
Y. Ma, T. Chen, and E. B. Fox · 2015
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Adam: A method for stochastic optimization
D. P. Kingma and J. Ba · 2015
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Distributed Bayesian Learning with Stochastic Natural-gradient Expectation Propagation and the Posterior Server
L. Hasenclever, S. Webb, T. Lienart, Y. Whye Teh, S. Vollmer, B. Lakshminarayanan, and C. Blundell · 2015
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Covariance-Controlled Adaptive Langevin Thermostat for Large-Scale Bayesian Sampling
X. Shang, Z. Zhu, B. Leimkuhler, and A. J. Storkey · 2015
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Measuring Sample Quality with Stein’s Method
J. Gorham and L. W. Mackey · 2015
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Stan: A probabilistic programming language
B. Carpenter, A. Gelman, M. Hoffman, D. Lee, B. Goodrich, M. Betancourt, M. A. Brubaker, J. Guo, P. Li, and A. Riddell · 2016
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On the difficulty of training recurrent neural networks
R. Pascanu, T. Mikolov, and Y. Bengio · 2013
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The no-u-turn sampler: Adaptively setting path lengths in hamiltonian monte carlo
M. D. Hoffman and A. Gelman · 2014
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Bayesian Sampling Using Stochastic Gradient Thermostats
N. Ding, Y. Fang, R. Babbush, C. Chen, R. D. Skeel, and H. Neven · 2014
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Stochastic Gradient Hamiltonian Monte Carlo
T. Chen, E. Fox, and C. Guestrin · 2014
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Stochastic processes and applications: Diffusion Processes, the Fokker-Planck and Langevin Equations
G. Pavliotis · 2014
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Adaptive Thermostats for Noisy Gradient Systems
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Stochastic Quasi-Newton Langevin Monte Carlo
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