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Stein Variational Gradient Descent With Matrix-Valued Kernels

arXiv 1910.12794 ↗First posted 28 Oct 2019stat.ML cs.LGcited by 32

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Abstract (arXiv)

Stein variational gradient descent (SVGD) is a particle-based inference algorithm that leverages gradient information for efficient approximate inference. In this work, we enhance SVGD by leveraging preconditioning matrices, such as the Hessian and Fisher information matrix, to incorporate geometric information into SVGD updates. We achieve this by presenting a generalization of SVGD that replaces the scalar-valued kernels in vanilla SVGD with more general matrix-valued kernels. This yields a significant extension of SVGD, and more importantly, allows us to flexibly incorporate various preconditioning matrices to accelerate the exploration in the probability landscape. Empirical results show that our method outperforms vanilla SVGD and a variety of baseline approaches over a range of real-world Bayesian inference tasks.

Key facts. Cited by 32 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Oct 2019.

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Citing papers per year: 2021: 7; 2022: 7; 2023: 4; 2024: 5; 2025: 4; 2026: 5.

32 papers.

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  1. 2021Robust Generalised Bayesian Inference for Intractable Likelihoodscited by 53
  2. 2021On Stein Variational Neural Network Ensemblescited by 21
  3. 2022Particle-based Variational Inference with Preconditioned Functional Gradient Flowcited by 20
  4. 2022Regularized Stein Variational Gradient Flowcited by 18
  5. 2021Sampling with Mirrored Stein Operatorscited by 17
  6. 2022Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Conditioncited by 16
  7. 2023Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descentcited by 13
  8. 2021Learning Equivariant Energy Based Models with Equivariant Stein Variational Gradient Descentcited by 10
  9. 2023Coin Sampling: Gradient-Based Bayesian Inference without Learning Ratescited by 8
  10. 2023Constrained Stein Variational Trajectory Optimizationcited by 8
  11. 2023Noise-Free Sampling Algorithms via Regularized Wasserstein Proximalscited by 7
  12. 2021Stein ICP for Uncertainty Estimation in Point Cloud Matchingcited by 6
20 more
  1. 2022A Note on the Convergence of Mirrored Stein Variational Gradient Descent under (L0,L1)-Smoothness Conditioncited by 4
  2. 2021Stein Variational Gradient Descent with Multiple Kernelcited by 3
  3. 2022Improved Stein Variational Gradient Descent with Importance Weightscited by 2
  4. 2024Electrostatics-based particle sampling and approximate inferencecited by 2
  5. 2024Stein Variational Evolution Strategiescited by 2
  6. 2026Dual-space posterior sampling for Bayesian inference in constrained inverse problemscited by 2
  7. 2021Tractable Computation of Expected Kernelscited by 1
  8. 2024Uncertainty Quantification of Graph Convolution Neural Network Models of Evolving Processescited by 1
  9. 2024ELBOing Stein: Variational Bayes with Stein Mixture Inferencecited by 1
  10. 2025Stein Diffusion Guidance: Training-Free Posterior Correction for Sampling Beyond High-Density Regionscited by 1
  11. 2025Soft Quality-Diversity Optimizationcited by 1
  12. 2022Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice modelscited by 0
  13. 2022Posterior sampling with CNN-based, Plug-and-Play regularization with applications to Post-Stack Seismic Inversioncited by 0
  14. 2024Stein Random Feature Regressioncited by 0
  15. 2025Accelerating Particle-based Energetic Variational Inferencecited by 0
  16. 2025Adaptive Kernel Selection for Stein Variational Gradient Descentcited by 0
  17. 2026Accelerated Regularized Wasserstein Proximal Sampling Algorithmscited by 0
  18. 2026Multirate Stein Variational Gradient Descent for Efficient Bayesian Samplingcited by 0
  19. 2026Stein Kernelized Molecular Dynamics for Active Learning of Interatomic Potentialscited by 0
  20. 2026Riesz-Kernel Stein Variational Gradient Descent: Renormalized Entropy and Long-Time Particle Limitscited by 0