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Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years.
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Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
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A spectral algorithm for learning mixture models
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Stochastic Differential Equations
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Sampling from strongly log-concave distributions with the Unadjusted Langevin Algorithm
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Local maxima in the likelihood of Gaussian mixture models: Structural results and algorithmic consequences
C. Jin, Y. Zhang, S. Balakrishnan, M. J. Wainwright, and M. I. Jordan · 2016
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Complexity bounds for Markov chain Monte Carlo algorithms via diffusion limits
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Lower bounds for finding stationary points I
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Theoretical guarantees for approximate sampling from smooth and log-concave densities
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Introductory Lectures on Convex Optimization: A Basic Course
Y. Nesterov · 2004
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Entropy Bounds and Isoperimetry
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Bayesian Modelling and Inference on Mixtures of Distributions
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Modified logarithmic Sobolev inequalities in discrete settings
S. G. Bobkov and P. Tetali · 2006
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On Isoperimetric Constants for Log-Concave Probability Distributions
S. G. Bobkov · 2007
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Optimal Transport: Old and New
C. Villani · 2009
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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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Nonasymptotic convergence analysis for the unadjusted Langevin algorithm
A. Durmus and E. Moulines · 2017
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Couplings and quantitative contraction rates for Langevin dynamics
A. Eberle, A. Guillin, and R. Zimmer · 2017
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Non-convex optimization for machine learning
P. Jain and P. Kar · 2017
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Rapid mixing of Hamiltonian Monte Carlo on strongly log-concave distributions
O. Mangoubi and A. Smith · 2017
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Non-convex learning via stochastic gradient Langevin dynamics: A nonasymptotic analysis
M. Raginsky, A. Rakhlin, and M. Telgarsky · 2017
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Coupling and convergence for Hamiltonian Monte Carlo
N. Bou-Rabee, A. Eberle, and R. Zimmer · 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
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Log-concave sampling: Metropolis-Hastings algorithms are fast!
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Non-asymptotic bounds for sampling algorithms without log-concavity
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Dimensionally tight running time bounds for second-order Hamiltonian Monte Carlo
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Is there an analog of Nesterov acceleration for MCMC?
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