Open Access
Issue
ESAIM: M2AN
Volume 58, Number 6, November-December 2024
Special issue - To commemorate Assyr Abdulle
Page(s) 2255 - 2286
DOI https://doi.org/10.1051/m2an/2024038
Published online 04 December 2024
  1. A. Abdulle, G. Vilmart and K.C. Zygalakis, Long time accuracy of Lie–Trotter splitting methods for Langevin dynamics. SIAM J. Numer. Anal. 53 (2015) 1–16. [CrossRef] [MathSciNet] [Google Scholar]
  2. J. Baker, P. Fearnhead, E.B. Fox and C. Nemeth, Control variates for stochastic gradient MCMC. Stat. Comput. 29 (2019) 599–615. [CrossRef] [MathSciNet] [Google Scholar]
  3. J. Besag, Discussion: Markov chains for exploring posterior distributions. Ann. Stat. 22 (1994) 1734–1741. [CrossRef] [Google Scholar]
  4. J. Bierkens, P. Fearnhead and G. Roberts, The zig–zag process and super-efficient sampling for Bayesian analysis of big data. Ann. Stat. 47 (2019) 1288–1320. [CrossRef] [Google Scholar]
  5. S.D. Bond and B.J. Leimkuhler, Molecular dynamics and the accuracy of numerically computed averages. Acta Numer. 16 (2007) 1–65. [CrossRef] [MathSciNet] [Google Scholar]
  6. N. Bou-Rabee and A. Eberle, Couplings for Andersen dynamics, in Annales de l’Institut Henri Poincare (B) Probabilites et statistiques. Vol. 58. Institut Henri Poincaré (2022) 916–944. [Google Scholar]
  7. N. Bou-Rabee and A. Eberle, Mixing time guarantees for unadjusted Hamiltonian Monte Carlo. Bernoulli 29 (2023) 75–104. [CrossRef] [MathSciNet] [Google Scholar]
  8. N. Bou-Rabee and M. Marsden, Unadjusted Hamiltonian MCMC with stratified Monte Carlo time integration. Preprint arXiv:2211.11003 (2022). [Google Scholar]
  9. N. Bou-Rabee, A. Eberle and R. Zimmer, Coupling and convergence for Hamiltonian Monte Carlo. Ann. Appl. Probab. 30 (2020) 1209–1250. [CrossRef] [MathSciNet] [Google Scholar]
  10. A. Bouchard-Côté, S.J. Vollmer and A. Doucet, The bouncy particle sampler: a nonreversible rejection-free Markov chain Monte Carlo method. J. Am. Stat. Assoc. 113 (2018) 855–867. [CrossRef] [Google Scholar]
  11. S. Boyd, S.P. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press (2004). [CrossRef] [Google Scholar]
  12. A. Brünger, C.L. Brooks III and M. Karplus, Stochastic boundary conditions for molecular dynamics simulations of ST2 water. Chem. Phys. Lett. 105 (1984) 495–500. [CrossRef] [Google Scholar]
  13. G. Bussi and M. Parrinello, Accurate sampling using Langevin dynamics. Phys. Rev. E 75 (2007) 056707. [CrossRef] [PubMed] [Google Scholar]
  14. Y. Cao, J. Lu and L. Wang, Complexity of randomized algorithms for underdamped Langevin dynamics. Commun. Math. Sci. 19 (2021) 1827–1853. [CrossRef] [MathSciNet] [Google Scholar]
  15. Y. Cao, J. Lu and L. Wang, On explicit l2-convergence rate estimate for underdamped Langevin dynamics. Arch. Ration. Mech. Anal. 247 (2023) 90. [CrossRef] [Google Scholar]
  16. S. Chandrasekhar, Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15 (1943) 1. [CrossRef] [Google Scholar]
  17. N. Chatterji, N. Flammarion, Y. Ma, P. Bartlett and M. Jordan, On the theory of variance reduction for stochastic gradient Monte Carlo, in International Conference on Machine Learning. PMLR (2018) 764–773. [Google Scholar]
  18. X. Cheng and P. Bartlett, Convergence of Langevin MCMC in KL-divergence, in Algorithmic Learning Theory. PMLR (2018) 186–211. [Google Scholar]
  19. X. Cheng, N.S. Chatterji, P.L. Bartlett and M.I. Jordan, Underdamped Langevin MCMC: a non-asymptotic analysis, in Conference on Learning Theory. PMLR (2018) 300–323. [Google Scholar]
  20. A. Dalalyan, Further and stronger analogy between sampling and optimization: Langevin Monte Carlo and gradient descent, in Conference on Learning Theory. PMLR (2017) 678–689. [Google Scholar]
  21. A.S. Dalalyan, Theoretical guarantees for approximate sampling from smooth and log-concave densities. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 79 (2017) 651–676. [CrossRef] [MathSciNet] [Google Scholar]
  22. A.S. Dalalyan and A. Karagulyan, User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient. Stochastic Process. App. 129 (2019) 5278–5311. [CrossRef] [Google Scholar]
  23. A.S. Dalalyan and L. Riou-Durand, On sampling from a log-concave density using kinetic Langevin diffusions. Bernoulli 26 (2020) 1956–1988. [CrossRef] [MathSciNet] [Google Scholar]
  24. G. Deligiannidis, D. Paulin, A. Bouchard-Côté and A. Doucet, Randomized Hamiltonian Monte Carlo as scaling limit of the bouncy particle sampler and dimension-free convergence rates. Ann. Appl. Probab. 31 (2021) 2612–2662. [CrossRef] [MathSciNet] [Google Scholar]
  25. A. Durmus and E. Moulines, Nonasymptotic convergence analysis for the unadjusted Langevin algorithm. Ann. Appl. Probab. 27 (2017) 1551–1587. [MathSciNet] [Google Scholar]
  26. A. Durmus and E. Moulines, High-dimensional Bayesian inference via the unadjusted Langevin algorithm. Bernoulli 25 (2019) 2854–2882. [CrossRef] [MathSciNet] [Google Scholar]
  27. A. Durmus, S. Majewski and B. Miasojedow, Analysis of Langevin Monte Carlo via convex optimization. J. Mach. Learn. Res. 20 (2019) 2666–2711. [Google Scholar]
  28. A. Durmus, A. Enfroy, É. Moulines and G. Stoltz, Uniform minorization condition and convergence bounds for discretizations of kinetic Langevin dynamics. Preprint arXiv:2107.14542 (2021). [Google Scholar]
  29. R. Dwivedi, Y. Chen, M.J. Wainwright and B. Yu, Log-concave sampling: Metropolis-hastings algorithms are fast! in Conference on Learning Theory. PMLR (2018) 793–797. [Google Scholar]
  30. A. Eberle, A. Guillin and R. Zimmer, Couplings and quantitative contraction rates for Langevin dynamics. Ann. Probab. 47 (2019) 1982–2010. [CrossRef] [MathSciNet] [Google Scholar]
  31. D.L. Ermak and H. Buckholz, Numerical integration of the Langevin equation: Monte Carlo simulation. J. Comput. Phys. 35 (1980) 169–182. [CrossRef] [MathSciNet] [Google Scholar]
  32. J. Finkelstein, G. Fiorin and B. Seibold, Comparison of modern Langevin integrators for simulations of coarse-grained polymer melts. Mol. Phys. 118 (2020) e1649493. [CrossRef] [Google Scholar]
  33. H. Furstenberg and H. Kesten, Products of random matrices. Ann. Math. Stat. 31 (1960) 457–469. [CrossRef] [Google Scholar]
  34. A. Gelman, J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari and D.B. Rubin, Bayesian Data Analysis. CRC Press (2013). [CrossRef] [Google Scholar]
  35. N. Gouraud, P. Le Bris, A. Majka and P. Monmarché, HMC and underdamped Langevin united in the unadjusted convex smooth case. Preprint arXiv:2202.00977 (2022). [Google Scholar]
  36. D. Griffeath, A maximal coupling for Markov chains. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 31 (1975) 95–106. [CrossRef] [Google Scholar]
  37. R. Johnson and T. Zhang, Accelerating stochastic gradient descent using predictive variance reduction. Adv. Neural Inf. Process. Syst. 26 (2013). [Google Scholar]
  38. V. Kargin, Products of random matrices: dimension and growth in norm. Ann. Appl. Probab. 23 (2010) 890–906. [Google Scholar]
  39. Y. LeCun, C. Cortes, C. Burges, et al., MNIST handwritten digit database (2010). [Google Scholar]
  40. B. Leimkuhler and C. Matthews, Rational construction of stochastic numerical methods for molecular sampling. Appl. Math./Res. eXpress 2013 (2013) 34–56. [Google Scholar]
  41. B. Leimkuhler and C. Matthews, Molecular Dynamics. Springer (2015). [Google Scholar]
  42. B. Leimkuhler, C. Matthews and M.V. Tretyakov, On the long-time integration of stochastic gradient systems. Proc. R. Soc. A Math. Phys. Eng. Sci. 470 (2014) 20140120. [Google Scholar]
  43. B. Leimkuhler, C. Matthews and G. Stoltz, The computation of averages from equilibrium and nonequilibrium Langevin molecular dynamics. IMA J. Numer. Anal. 36 (2016) 13–79. [MathSciNet] [Google Scholar]
  44. B. Leimkuhler, D. Paulin and P.A. Whalley, Contraction and convergence rates for discretized kinetic Langevin dynamics. SIAM J. Numer. Anal. 62 (2024) 1226–1258. [CrossRef] [MathSciNet] [Google Scholar]
  45. M.B. Majka, A. Mijatović and L. Szpruch, Nonasymptotic bounds for sampling algorithms without log-concavity. Ann. Appl. Probab. 30 (2020) 1534–1581. [CrossRef] [MathSciNet] [Google Scholar]
  46. S. Melchionna, Design of quasisymplectic propagators for Langevin dynamics. J. Chem. Phys. 127 (2007) 044108. [CrossRef] [PubMed] [Google Scholar]
  47. P. Monmarché, High-dimensional MCMC with a standard splitting scheme for the underdamped Langevin diffusion. Electron. J. Stat. 15 (2021) 4117–4166. [MathSciNet] [Google Scholar]
  48. P. Monmarché, Almost sure contraction for diffusions on ℝd. Application to generalized Langevin diffusions Stoch. Process. App. 161 (2023) 316–349. [Google Scholar]
  49. C. Nemeth and P. Fearnhead, Stochastic gradient Markov chain Monte Carlo. J. Am. Stat. Assoc. 116 (2021) 433–450. [CrossRef] [Google Scholar]
  50. G.A. Pavliotis, Stochastic Processes and Applications: Diffusion Processes, the Fokker–Planck and Langevin Equations. Vol. 60. Springer (2014). [CrossRef] [Google Scholar]
  51. E.A.J.F. Peters and G. de With, Rejection-free Monte Carlo sampling for general potentials. Phys. Rev. E 85 (2012) 026703. [CrossRef] [PubMed] [Google Scholar]
  52. M. Quiroz, R. Kohn, M. Villani and M.-N. Tran, Speeding up MCMC by efficient data subsampling. J. Am. Stat. Assoc. 114 (2019) 831–843. [CrossRef] [Google Scholar]
  53. L. Riou-Durand and J. Vogrinc, Metropolis adjusted Langevin trajectories: a robust alternative to Hamiltonian Monte Carlo. Preprint arXiv:2202.13230 (2022). [Google Scholar]
  54. H. Robbins and S. Monro, A stochastic approximation method. Ann. Math. Stat. 22 (1951) 400–407. [CrossRef] [Google Scholar]
  55. G.O. Roberts and R.L. Tweedie, Exponential convergence of Langevin distributions and their discrete approximations. Bernoulli 2 (1996) 341–363. [CrossRef] [Google Scholar]
  56. P.J. Rossky, J.D. Doll and H.L. Friedman, Brownian dynamics as smart Monte Carlo simulation. J. Chem. Phys. 69 (1978) 4628–4633. [CrossRef] [Google Scholar]
  57. J.M. Sanz Serna and K.C. Zygalakis, Contractivity of Runge–Kutta methods for convex gradient systems. SIAM J. Numer. Anal. 58 (2020) 2079–2092. [CrossRef] [MathSciNet] [Google Scholar]
  58. J.M. Sanz-Serna and K.C. Zygalakis, Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations. J. Mach. Learn. Res. 22 (2021) 1–37. [Google Scholar]
  59. K. Schuh, Global contractivity for Langevin dynamics with distribution-dependent forces and uniform in time propagation of Chaos. Annales de l’Institut Henri Poincare (B) Probabilites et statistiques. Vol. 60. Institut Henri Poincaré (2024) 753–789. [Google Scholar]
  60. I. Sekkat and G. Stoltz, Quantifying the mini-batching error in Bayesian inference for adaptive Langevin dynamics. J. Mach. Learn. Res. 24 (2023) 58. [MathSciNet] [Google Scholar]
  61. R. Shen and Y.T. Lee, The randomized midpoint method for log-concave sampling. Adv. Neural Inf. Process. Syst. 32 (2019). [Google Scholar]
  62. R.D. Skeel and J.A. Izaguirre, An impulse integrator for Langevin dynamics. Mol. Phys. 100 (2002) 3885–3891. [CrossRef] [Google Scholar]
  63. L. Vaserstein, Markovian processes on countable space product describing large systems of automata. Probl. Peredachi Inf. 5 (1969) 64–72. [Google Scholar]
  64. D. Vats, J.M. Flegal and G.L. Jones, Multivariate output analysis for Markov chain Monte Carlo. Biometrika 106 (2019) 321–337. [CrossRef] [MathSciNet] [Google Scholar]
  65. C. Villani, Optimal Transport: Old and New. Vol. 338. Springer (2009). [CrossRef] [Google Scholar]
  66. S.J. Vollmer, K.C. Zygalakis and Y.W. Teh, Exploration of the (non-) asymptotic bias and variance of stochastic gradient Langevin dynamics. J. Mach. Learn. Res. 17 (2016) 5504–5548. [Google Scholar]
  67. M. Welling and Y.W. Teh, Bayesian learning via stochastic gradient Langevin dynamics, in Proceedings of the 28th International Conference on Machine Learning (ICML-11) (2011) 681–688. [Google Scholar]
  68. M. Zhang, S. Chewi, M.B. Li, K. Balasubramanian and M.A. Erdogdu, Improved discretization analysis for under-damped Langevin Monte Carlo. The Thirty Sixth Annual Conference on Learning Theory. PMLR (2023) 36–71. [Google Scholar]

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