mlsanityData to 14 Oct 2026

Theoretical guarantees for approximate sampling from smooth and log-concave densities

arXiv 1412.7392 ↗First posted 23 Dec 2014stat.CO math.ST stat.MLcited by 208

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Abstract (arXiv)

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling from a given distribution is impossible or computationally expensive and, therefore, one needs to resort to approximate sampling strategies. However, there is no well-developed theory providing meaningful nonasymptotic guarantees for the approximate sampling procedures, especially in the high-dimensional problems. This paper makes some progress in this direction by considering the problem of sampling from a distribution having a smooth and log-concave density defined on (RRp), for some integer (p>0). We establish nonasymptotic bounds for the error of approximating the target distribution by the one obtained by the Langevin Monte Carlo method and its variants. We illustrate the effectiveness of the established guarantees with various experiments. Underlying our analysis are insights from the theory of continuous-time diffusion processes, which may be of interest beyond the framework of log-concave densities considered in the present work.

Key facts. Cited by 208 papers in the map (data through 14 Oct 2026). First posted on arXiv 23 Dec 2014.

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Citing papers per year: 2021: 31; 2022: 37; 2023: 40; 2024: 38; 2025: 32; 2026: 30.

208 papers.

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  1. 2022Convergence of denoising diffusion models under the manifold hypothesiscited by 242
  2. 2022Convergence for score-based generative modeling with polynomial complexitycited by 177
  3. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 97
  4. 2021Annealed Flow Transport Monte Carlocited by 90
  5. 2022Variational inference via Wasserstein gradient flowscited by 85
  6. 2021Differential Privacy Dynamics of Langevin Diffusion and Noisy Gradient Descentcited by 73
  7. 2022Privacy of Noisy Stochastic Gradient Descent: More Iterations without More Privacy Losscited by 61
  8. 2024Optimal score estimation via empirical Bayes smoothingcited by 61
  9. 2022Convex Analysis of the Mean Field Langevin Dynamicscited by 55
  10. 2022Score-based Generative Modeling Secretly Minimizes the Wasserstein Distancecited by 50
  11. 2022Private Convex Optimization via Exponential Mechanismcited by 49
  12. 2021Minimax Mixing Time of the Metropolis-Adjusted Langevin Algorithm for Log-Concave Samplingcited by 44
38 more
  1. 2021Differentiable Annealed Importance Sampling and the Perils of Gradient Noisecited by 36
  2. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  3. 2022FedPop: A Bayesian Approach for Personalised Federated Learningcited by 35
  4. 2023Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincar'e Inequalitycited by 31
  5. 2022Birth-death dynamics for sampling: Global convergence, approximations and their asymptoticscited by 30
  6. 2023Improved dimension dependence of a proximal algorithm for samplingcited by 30
  7. 2023Provable and Practical: Efficient Exploration in Reinforcement Learning via Langevin Monte Carlocited by 29
  8. 2025Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distancecited by 29
  9. 2023Improved Discretization Analysis for Underdamped Langevin Monte Carlocited by 28
  10. 2024Stochastic Localization via Iterative Posterior Samplingcited by 28
  11. 2021QLSD: Quantised Langevin stochastic dynamics for Bayesian federated learningcited by 26
  12. 2022Particle algorithms for maximum likelihood training of latent variable modelscited by 26
  13. 2023Towards Predicting Equilibrium Distributions for Molecular Systems with Deep Learningcited by 26
  14. 2021Sqrt(d) Dimension Dependence of Langevin Monte Carlocited by 25
  15. 2022Convergence of the Riemannian Langevin Algorithmcited by 25
  16. 2021A Proximal Algorithm for Sampling from Non-smooth Potentialscited by 24
  17. 2024Implicit Diffusion: Efficient Optimization through Stochastic Samplingcited by 24
  18. 2022A Proximal Algorithm for Samplingcited by 22
  19. 2022Langevin Monte Carlo for Contextual Banditscited by 22
  20. 2022Resolving the Mixing Time of the Langevin Algorithm to its Stationary Distribution for Log-Concave Samplingcited by 22
  21. 2021A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1cited by 21
  22. 2023Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reductioncited by 20
  23. 2021Lower Bounds on Metropolized Sampling Methods for Well-Conditioned Distributionscited by 19
  24. 2021The query complexity of sampling from strongly log-concave distributions in one dimensioncited by 18
  25. 2022Self-Consistency of the Fokker-Planck Equationcited by 18
  26. 2023Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimationcited by 17
  27. 2022Improved Convergence Rate of Stochastic Gradient Langevin Dynamics with Variance Reduction and its Application to Optimizationcited by 16
  28. 2022Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Conditioncited by 16
  29. 2023When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?cited by 15
  30. 2021Lazy OCO: Online Convex Optimization on a Switching Budgetcited by 14
  31. 2021On Convergence of Federated Averaging Langevin Dynamicscited by 14
  32. 2023Chain of Log-Concave Markov Chainscited by 14
  33. 2022Denoising MCMC for Accelerating Diffusion-Based Generative Modelscited by 13
  34. 2022Controlling Moments with Kernel Stein Discrepanciescited by 13
  35. 2024Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalitiescited by 13
  36. 2024Entropy contraction of the Gibbs sampler under log-concavitycited by 13
  37. 2021When is the Convergence Time of Langevin Algorithms Dimension Independent? A Composite Optimization Viewpointcited by 12
  38. 2023Query lower bounds for log-concave samplingcited by 12

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