mlsanityData to 7 Oct 2026

Accelerated Information Gradient flow

arXiv 1909.02102 ↗First posted 4 Sep 2019math.OC cs.IT math.ITcited by 38

Not on the map. Why?

Abstract (arXiv)

We present a framework for Nesterov's accelerated gradient flows in probability space to design efficient mean-field Markov chain Monte Carlo (MCMC) algorithms for Bayesian inverse problems. Here four examples of information metrics are considered, including Fisher-Rao metric, Wasserstein-2 metric, Kalman-Wasserstein metric and Stein metric. For both Fisher-Rao and Wasserstein-2 metrics, we prove convergence properties of accelerated gradient flows. In implementations, we propose a sampling-efficient discrete-time algorithm for Wasserstein-2, Kalman-Wasserstein and Stein accelerated gradient flows with a restart technique. We also formulate a kernel bandwidth selection method, which learns the gradient of logarithm of density from Brownian-motion samples. Numerical experiments, including Bayesian logistic regression and Bayesian neural network, show the strength of the proposed methods compared with state-of-the-art algorithms.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Sep 2019.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 3; 2023: 10; 2024: 9; 2025: 6; 2026: 5.

38 papers.

Sort:

By area:

  1. 2021Annealed Flow Transport Monte Carlocited by 90
  2. 2023A Computational Framework for Solving Wasserstein Lagrangian Flowscited by 43
  3. 2023A mean-field games laboratory for generative modelingcited by 28
  4. 2022Particle algorithms for maximum likelihood training of latent variable modelscited by 26
  5. 2021Projected Wasserstein gradient descent for high-dimensional Bayesian inferencecited by 24
  6. 2022Particle-based Variational Inference with Preconditioned Functional Gradient Flowcited by 20
  7. 2023Sampling via Gradient Flows in the Space of Probability Measurescited by 20
  8. 2023Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariancecited by 16
  9. 2023Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descentcited by 13
  10. 2024Constrained Sampling with Primal-Dual Langevin Monte Carlocited by 10
  11. 2021Scaling Up Bayesian Uncertainty Quantification for Inverse Problems using Deep Neural Networkscited by 9
  12. 2022Provably convergent quasistatic dynamics for mean-field two-player zero-sum gamescited by 9
26 more
  1. 2023Accelerating optimization over the space of probability measurescited by 9
  2. 2023GAD-PVI: A General Accelerated Dynamic-Weight Particle-Based Variational Inference Frameworkcited by 9
  3. 2021DPVI: A Dynamic-Weight Particle-Based Variational Inference Frameworkcited by 7
  4. 2023Noise-Free Sampling Algorithms via Regularized Wasserstein Proximalscited by 7
  5. 2024Importance Corrected Neural JKO Samplingcited by 7
  6. 2024Score-based Neural Ordinary Differential Equations for Computing Mean Field Control Problemscited by 7
  7. 2025Accelerated Stein Variational Gradient Flowcited by 5
  8. 2024Ensemble-Based Annealed Importance Samplingcited by 4
  9. 2021De-randomizing MCMC dynamics with the diffusion Stein operatorcited by 3
  10. 2024Rethinking the Diffusion Models for Numerical Tabular Data Imputation from the Perspective of Wasserstein Gradient Flowcited by 3
  11. 2024A Particle Algorithm for Mean-Field Variational Inferencecited by 3
  12. 2025Towards understanding Accelerated Stein Variational Gradient Flow -- Analysis of Generalized Bilinear Kernels for Gaussian target distributionscited by 2
  13. 2024Sampling with Adaptive Variance for Multimodal Distributionscited by 1
  14. 2025Nesterov Acceleration for Ensemble Kalman Inversion and Variantscited by 1
  15. 2025Preconditioned Regularized Wasserstein Proximal Samplingcited by 1
  16. 2025Hessian-guided Perturbed Wasserstein Gradient Flows for Escaping Saddle Pointscited by 1
  17. 2026A Kernel Approach for Semi-implicit Variational Inferencecited by 1
  18. 2026Accelerated Multiple Wasserstein Gradient Flows for Multi-objective Distributional Optimizationcited by 1
  19. 2023Information geometric bound on general chemical reaction networkscited by 0
  20. 2023Scaling Limits of the Wasserstein information matrix on Gaussian Mixture Modelscited by 0
  21. 2024Continuous-time Riemannian SGD and SVRG Flows on Wasserstein Probabilistic Spacecited by 0
  22. 2024Deterministic Fokker-Planck Transport -- With Applications to Sampling, Variational Inference, Kernel Mean Embeddings & Sequential Monte Carlocited by 0
  23. 2025Accelerated Markov Chain Monte Carlo Algorithms on Discrete Statescited by 0
  24. 2026Accelerated Regularized Wasserstein Proximal Sampling Algorithmscited by 0
  25. 2026Well-Posed KL-Regularized Control via Wasserstein and Kalman-Wasserstein KL Divergencescited by 0
  26. 2026SympFormer: Accelerated attention blocks via Inertial Dynamics on Density Manifoldscited by 0