On stochastic gradient Langevin dynamics with dependent data streams in the logconcave case

DOI10.3150/19-BEJ1187zbMath1475.60156arXiv1812.02709OpenAlexW3109128007MaRDI QIDQ2214233

Miklós Rásonyi, Eric Moulines, Ying Zhang, Sotirios Sabanis, M. Barkhagen, N. H. Chau

Publication date: 7 December 2020

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.02709

zbMATH Keywords

stochastic approximationMonte Carlo methods\(L\)-mixingLangevin diffusion

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion processes (60J60) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

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Cites Work

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• Existence and stability for Fokker-Planck equations with log-concave reference measure
• Strong approximation of the recursive prediction error estimator of the parameters of an ARMA process
• On Rissanen's predictive stochastic complexity for stationary ARMA processes
• Exponential convergence of Langevin distributions and their discrete approximations
• Introductory lectures on convex optimization. A basic course.
• User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient
• High-dimensional Bayesian inference via the unadjusted Langevin algorithm
• Nonasymptotic convergence analysis for the unadjusted Langevin algorithm
• Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise.
• Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
• A Remark on Stirling's Formula
• A Representation Theorem for the Error of Recursive Estimators
• On the statistical analysis of quantized Gaussian AR(1) processes
• On a class of mixing processes
• AR( infinity ) estimation and nonparametric stochastic complexity
• On fixed gain recursive estimators with discontinuity in the parameters
• Theoretical Guarantees for Approximate Sampling from Smooth and Log-Concave Densities
• Optimal Transport