Extends high-dimensional KRR to product kernels, proving convergence rates that recover minimax optimality for source condition s ≤ 1, saturation for s > 1, and multiple-descent phenomena with respect to sample size n.
Foundations of Computational Mathematics , volume=
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Sobolev regularization on the witness function enables global convergence of MMD gradient flows for both sampling and generative modeling without isoperimetric assumptions.
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.
An augmented kernel ridge regression estimator separates linear and nonlinear components to achieve sharp oracle inequalities and minimax optimal prediction risk under general kernels.
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Large Dimensional Kernel Ridge Regression: Extending to Product Kernels
Extends high-dimensional KRR to product kernels, proving convergence rates that recover minimax optimality for source condition s ≤ 1, saturation for s > 1, and multiple-descent phenomena with respect to sample size n.
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Sobolev Regularized MMD Gradient Flow
Sobolev regularization on the witness function enables global convergence of MMD gradient flows for both sampling and generative modeling without isoperimetric assumptions.
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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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Adaptive Kernel Ridge Regression with Linear Structure: Sharp Oracle Inequalities and Minimax Optimality
An augmented kernel ridge regression estimator separates linear and nonlinear components to achieve sharp oracle inequalities and minimax optimal prediction risk under general kernels.