Towards understanding the dynamics of gaussian-stein variational gradient descent

T Liu, P Ghosal… - Advances in Neural …, 2024 - proceedings.neurips.cc
Abstract Stein Variational Gradient Descent (SVGD) is a nonparametric particle-based
deterministic sampling algorithm. Despite its wide usage, understanding the theoretical …

Birth–death dynamics for sampling: global convergence, approximations and their asymptotics

Y Lu, D Slepčev, L Wang - Nonlinearity, 2023 - iopscience.iop.org
Motivated by the challenge of sampling Gibbs measures with nonconvex potentials, we
study a continuum birth–death dynamics. We improve results in previous works (Liu et al …

Stein transport for Bayesian inference

N Nüsken - arXiv preprint arXiv:2409.01464, 2024 - arxiv.org
We introduce $\textit {Stein transport} $, a novel methodology for Bayesian inference
designed to efficiently push an ensemble of particles along a predefined curve of tempered …

Efficient, multimodal, and derivative-free bayesian inference with Fisher–Rao gradient flows

Y Chen, DZ Huang, J Huang, S Reich… - Inverse Problems, 2024 - iopscience.iop.org
In this paper, we study efficient approximate sampling for probability distributions known up
to normalization constants. We specifically focus on a problem class arising in Bayesian …

Kernel approximation of Fisher-Rao gradient flows

JJ Zhu, A Mielke - arXiv preprint arXiv:2410.20622, 2024 - arxiv.org
The purpose of this paper is to answer a few open questions in the interface of kernel
methods and PDE gradient flows. Motivated by recent advances in machine learning …

Sampling in Unit Time with Kernel Fisher-Rao Flow

A Maurais, Y Marzouk - arXiv preprint arXiv:2401.03892, 2024 - arxiv.org
We introduce a new mean-field ODE and corresponding interacting particle systems for
sampling from an unnormalized target density or Bayesian posterior. The interacting particle …

Neural sampling from Boltzmann densities: Fisher-Rao curves in the Wasserstein geometry

J Chemseddine, C Wald, R Duong, G Steidl - arXiv preprint arXiv …, 2024 - arxiv.org
We deal with the task of sampling from an unnormalized Boltzmann density $\rho_D $ by
learning a Boltzmann curve given by energies $ f_t $ starting in a simple density $\rho_Z …

Measure transport with kernel mean embeddings

L Wang, N Nüsken - arXiv preprint arXiv:2401.12967, 2024 - arxiv.org
Kalman filters constitute a scalable and robust methodology for approximate Bayesian
inference, matching first and second order moments of the target posterior. To improve the …

Convergence and stability results for the particle system in the stein gradient descent method

JA Carrillo, J Skrzeczkowski - arXiv preprint arXiv:2312.16344, 2023 - arxiv.org
There has been recently a lot of interest in the analysis of the Stein gradient descent method,
a deterministic sampling algorithm. It is based on a particle system moving along the …

Differential Equation–Constrained Optimization with Stochasticity

Q Li, L Wang, Y Yang - SIAM/ASA Journal on Uncertainty Quantification, 2024 - SIAM
Most inverse problems from physical sciences are formulated as PDE-constrained
optimization problems. This involves identifying unknown parameters in equations by …