Mean-field SVGD flow converges locally at explicit polynomial L2 rates to the target on the torus for Riesz kernels, with rates depending on dimension and regularity, sharpness in some regimes, and recovery of global exponential convergence for Coulomb kernels.
Scaling limit of the
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Energy-based model with covariance regularization computes normalized posteriors for linear inverse problems without retraining, enabling adaptive sampling and blind estimation on image datasets.
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Quantitative Local Convergence of Mean-Field Stein Variational Gradient Flow
Mean-field SVGD flow converges locally at explicit polynomial L2 rates to the target on the torus for Riesz kernels, with rates depending on dimension and regularity, sharpness in some regimes, and recovery of global exponential convergence for Coulomb kernels.
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Learning Normalized Energy Models for Linear Inverse Problems
Energy-based model with covariance regularization computes normalized posteriors for linear inverse problems without retraining, enabling adaptive sampling and blind estimation on image datasets.