Tag: finite
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Finite-Particle Rates for Regularized Stein Variational Gradient Descent
Finite-Particle Rates for Regularized Stein Variational Gradient Descent arXiv:2602.05172v1 Announce Type: new Abstract: We derive finite-particle rates for the regularized Stein variational gradient descent (R-SVGD) algorithm introduced by He et al. (2024) that corrects the constant-order bias of the SVGD by applying a resolvent-type preconditioner to the kernelized Wasserstein gradient. For the resulting interacting $N$-particle…
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Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weights
Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weights arXiv:2507.12686v1 Announce Type: new Abstract: We study the Finite-Dimensional Distributions (FDDs) of deep neural networks with randomly initialized weights that have finite-order moments. Specifically, we establish Gaussian approximation bounds in the Wasserstein-$1$ norm between the FDDs and their Gaussian limit assuming a Lipschitz activation…
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Learning Linearized Models from Nonlinear Systems under Initialization Constraints with Finite Data
Learning Linearized Models from Nonlinear Systems under Initialization Constraints with Finite Data arXiv:2505.04954v1 Announce Type: new Abstract: The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system trajectory under i.i.d.…
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How well behaved is finite dimensional Diffusion Maps?
How well behaved is finite dimensional Diffusion Maps? arXiv:2412.03992v1 Announce Type: new Abstract: Under a set of assumptions on a family of submanifolds $subset {mathbb R}^D$, we derive a series of geometric properties that remain valid after finite-dimensional and almost isometric Diffusion Maps (DM), including almost uniform density, finite polynomial approximation and local reach. Leveraging…