mlsanityData to 7 Oct 2026

Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations

arXiv 2104.12384 ↗First posted 26 Apr 2021stat.ML cs.LG cs.NAcited by 8

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Abstract (arXiv)

We present a framework that allows for the non-asymptotic study of the 2-Wasserstein distance between the invariant distribution of an ergodic stochastic differential equation and the distribution of its numerical approximation in the strongly log-concave case. This allows us to study in a unified way a number of different integrators proposed in the literature for the overdamped and underdamped Langevin dynamics. In addition, we analyse a novel splitting method for the underdamped Langevin dynamics which only requires one gradient evaluation per time step. Under an additional smoothness assumption on a d--dimensional strongly log-concave distribution with condition number kappa, the algorithm is shown to produce with an Obig(kappa5/4 d1/4ε-1/2 big) complexity samples from a distribution that, in Wasserstein distance, is at most ε>0 away from the target distribution.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 18 of its 53 references that are in the map. First posted on arXiv 26 Apr 2021.

Builds on

18 of 53 references.

References · 18

  1. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  2. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 195
  3. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 144
  4. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 131
  5. 2018Analysis of Langevin Monte Carlo via convex optimizationcited by 126
  6. 2017User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradientcited by 116
  7. 2014Analysis and Design of Optimization Algorithms via Integral Quadratic Constraintscited by 105
  8. 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 77
  9. 2018On sampling from a log-concave density using kinetic Langevin diffusionscited by 61
  10. 2019High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithmcited by 36
  11. 2018Non-asymptotic bounds for sampling algorithms without log-concavitycited by 35
  12. 2017Geometric integrators and the Hamiltonian Monte Carlo methodcited by 25
6 more
  1. 2017Analysis of Optimization Algorithms via Integral Quadratic Constraints: Nonstrongly Convex Problemscited by 19
  2. 2019Bounding the error of discretized Langevin algorithms for non-strongly log-concave targetscited by 16
  3. 2020The connections between Lyapunov functions for some optimization algorithms and differential equationscited by 11
  4. 2019Spectral Density-Based and Measure-Preserving ABC for partially observed diffusion processes. An illustration on Hamiltonian SDEscited by 7
  5. 2019Implicit Langevin Algorithms for Sampling From Log-concave Densitiescited by 6
  6. 2019Contractivity of Runge-Kutta methods for convex gradient systemscited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 4; 2025: 2; 2026: 1.

8 papers.

  1. 2023Momentum Particle Maximum Likelihoodcited by 12
  2. 2024Sampling from Bayesian Neural Network Posteriors with Symmetric Minibatch Splitting Langevin Dynamicscited by 12
  3. 2024Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equationscited by 3
  4. 2024Single-seed generation of Brownian paths and integrals for adaptive and high order SDE solverscited by 3
  5. 2025Randomised Splitting Methods and Stochastic Gradient Descentcited by 3
  6. 2024Correction to "Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations"cited by 2
  7. 2025Random Reshuffling for Stochastic Gradient Langevin Dynamicscited by 2
  8. 2026Kinetic Langevin Splitting Schemes for Constrained Samplingcited by 0