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DOI10.1137/20M1356002zbMath1475.62292arXiv2007.13869OpenAlexW3159369427MaRDI QIDQ4999394

Roger G. Ghanem, Ruda Zhang

Publication date: 6 July 2021

Published in: SIAM Journal on Mathematics of Data Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.13869

zbMATH Keywords

resamplingprobabilistic learningdata augmentationdata manifold

Mathematics Subject Classification ID

Statistics on manifolds (62R30) Nonparametric statistical resampling methods (62G09) Learning and adaptive systems in artificial intelligence (68T05) Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Computational methods for attractors of dynamical systems (37M22)

Related Items (2)

Data driven Dirichlet sampling on manifolds ⋮ Gaussian Process Subspace Prediction for Model Reduction

Uses Software

• bootstrap
• PRMLT

Cites Work

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• Nonparametric modal regression
• Manifold estimation and singular deconvolution under Hausdorff loss
• Differential geometry and mathematical physics. I: Manifolds, Lie groups and Hamiltonian systems
• Nonparametric ridge estimation
• Data-driven probability concentration and sampling on manifold
• Asymptotic theory for density ridges
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Jackknife, bootstrap and other resampling methods in regression analysis
• Statistics on special manifolds
• Sampling of Bayesian posteriors with a non-Gaussian probabilistic learning on manifolds from a small dataset
• Hybrid Monte Carlo methods for sampling probability measures on submanifolds
• The geometric foundations of Hamiltonian Monte Carlo
• Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis
• Geodesic Monte Carlo on Embedded Manifolds
• Introduction to Smooth Manifolds
• On Multiple Eigenvalues of Matrices Depending on Several Parameters
• Differential Topology
• Monte Carlo on Manifolds: Sampling Densities and Integrating Functions
• Principal Curves
• Nonparametric Inference on Manifolds
• Convergence of the Iterates of Descent Methods for Analytic Cost Functions
• Sampling from a Manifold

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