User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient

DOI10.1016/j.spa.2019.02.016zbMath1428.62316arXiv1710.00095OpenAlexW2963599479WikidataQ128260590 ScholiaQ128260590MaRDI QIDQ2280028

Arnak S. Dalalyan, Avetik Karagulyan

Publication date: 17 December 2019

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.00095

zbMATH Keywords

Markov chain Monte Carlorates of convergencegradient descentLangevin algorithmapproximate sampling

Mathematics Subject Classification ID

Computational methods for problems pertaining to statistics (62-08) Estimation in multivariate analysis (62H12) Linear regression; mixed models (62J05) Monte Carlo methods (65C05) Diffusion processes (60J60)

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Cites Work

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• Criteria for recurrence and existence of invariant measures for multidimensional diffusions
• Exponential convergence of Langevin distributions and their discrete approximations
• Langevin diffusions and Metropolis-Hastings algorithms
• Introductory lectures on convex optimization. A basic course.
• Geometric ergodicity of Metropolis algorithms
• Sampling from a log-concave distribution with projected Langevin Monte Carlo
• Normalizing constants of log-concave densities
• Langevin-type models. I: Diffusions with given stationary distributions and their discretizations
• Langevin-type models II: Self-targeting candidates for MCMC algorithms
• Sampling from non-smooth distributions through Langevin diffusion
• High-dimensional Bayesian inference via the unadjusted Langevin algorithm
• Nonasymptotic convergence analysis for the unadjusted Langevin algorithm
• Pathwise optimal transport bounds between a one-dimensional diffusion and its Euler scheme
• Optimal transport bounds between the time-marginals of a multidimensional diffusion and its Euler scheme
• Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels
• Optimal Scaling of Discrete Approximations to Langevin Diffusions
• A variational perspective on accelerated methods in optimization
• Efficient Bayesian Computation by Proximal Markov Chain Monte Carlo: When Langevin Meets Moreau
• Sampling can be faster than optimization
• Theoretical Guarantees for Approximate Sampling from Smooth and Log-Concave Densities

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