mlsanityData to 7 Oct 2026

Projected Wasserstein gradient descent for high-dimensional Bayesian inference

arXiv 2102.06350 ↗First posted 12 Feb 2021cs.LG stat.MLcited by 24

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Abstract (arXiv)

We propose a projected Wasserstein gradient descent method (pWGD) for high-dimensional Bayesian inference problems. The underlying density function of a particle system of WGD is approximated by kernel density estimation (KDE), which faces the long-standing curse of dimensionality. We overcome this challenge by exploiting the intrinsic low-rank structure in the difference between the posterior and prior distributions. The parameters are projected into a low-dimensional subspace to alleviate the approximation error of KDE in high dimensions. We formulate a projected Wasserstein gradient flow and analyze its convergence property under mild assumptions. Several numerical experiments illustrate the accuracy, convergence, and complexity scalability of pWGD with respect to parameter dimension, sample size, and processor cores.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 23 of its 51 references that are in the map. First posted on arXiv 12 Feb 2021.

Builds on

23 of 51 references.

References · 23

  1. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  2. 2017Stein Variational Gradient Descent as Gradient Flowcited by 149
  3. 2020Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimationcited by 87
  4. 2019On the geometry of Stein variational gradient descentcited by 82
  5. 2018A Stein variational Newton methodcited by 49
  6. 2020Derivative-Informed Projected Neural Networks for High-Dimensional Parametric Maps Governed by PDEscited by 40
  7. 2019Accelerated Information Gradient flowcited by 38
  8. 2014Dimension-independent likelihood-informed MCMCcited by 36
  9. 2020Projected Stein Variational Gradient Descentcited by 33
  10. 2013A computational framework for infinite-dimensional Bayesian inverse problems. Part I: The linearized case, with application to global seismic inversioncited by 32
  11. 2018Certified dimension reduction in nonlinear Bayesian inverse problemscited by 26
  12. 2020Information Newton's flow: second-order optimization method in probability spacecited by 22
11 more
  1. 2019Projected Stein Variational Newton: A Fast and Scalable Bayesian Inference Method in High Dimensionscited by 21
  2. 2019Is There an Analog of Nesterov Acceleration for MCMC?cited by 19
  3. 2014A Fast and Scalable Method for A-Optimal Design of Experiments for Infinite-dimensional Bayesian Nonlinear Inverse Problemscited by 14
  4. 2016Stochastic Gradient MCMC with Stale Gradientscited by 9
  5. 2020A fast and scalable computational framework for large-scale and high-dimensional Bayesian optimal experimental designcited by 9
  6. 2017Nonreversible Langevin Samplers: Splitting Schemes, Analysis and Implementationcited by 8
  7. 2020Optimal design of acoustic metamaterial cloaks under uncertaintycited by 7
  8. 2018Taylor approximation and variance reduction for PDE-constrained optimal control under uncertaintycited by 5
  9. 2016Mean-variance risk-averse optimal control of systems governed by PDEs with random parameter fields using quadratic approximationscited by 4
  10. 2016A-optimal encoding weights for nonlinear inverse problems, with applications to the Helmholtz inverse problemcited by 3
  11. 2020Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilitiescited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 4; 2023: 7; 2024: 4; 2025: 3; 2026: 3.

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  1. 2021Repulsive Deep Ensembles are Bayesiancited by 103
  2. 2021Optimizing Functionals on the Space of Probabilities with Input Convex Neural Networkscited by 53
  3. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  4. 2021Efficient Gradient Flows in Sliced-Wasserstein Spacecited by 21
  5. 2022Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problemscited by 21
  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. 2022Optimal Neural Network Approximation of Wasserstein Gradient Direction via Convex Optimizationcited by 9
  11. 2022Feature Space Particle Inference for Neural Network Ensemblescited by 9
  12. 2023The Score-Difference Flow for Implicit Generative Modelingcited by 9
12 more
  1. 2023Minimizing f-Divergences by Interpolating Velocity Fieldscited by 8
  2. 2024Path-Guided Particle-based Samplingcited by 8
  3. 2025Visual Prompting for One-shot Controllable Video Editing without Inversioncited by 8
  4. 2023Input-gradient space particle inference for neural network ensemblescited by 7
  5. 2024Wasserstein Gradient Boosting: A Framework for Distribution-Valued Supervised Learningcited by 4
  6. 2024Forward-Euler time-discretization for Wasserstein gradient flows can be wrongcited by 3
  7. 2024A Library of Mirrors: Deep Neural Nets in Low Dimensions are Convex Lasso Models with Reflection Featurescited by 1
  8. 2025Sequential Bayesian Design for Efficient Surrogate Construction in the Inversion of Darcy Flowscited by 1
  9. 2026Radon--Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensionscited by 1
  10. 2025Liouville PDE-based sliced-Wasserstein flowcited by 0
  11. 2026Nesterov acceleration in optimizing over probability measurescited by 0
  12. 2026Wasserstein Gradient Flows and Forward-Only Diffusion Are Not Enough for Multimodal Samplingcited by 0