Mercer Kernels and Integrated Variance Experimental Design: Connections Between Gaussian Process Regression and Polynomial Approximation
From MaRDI portal
Publication:5741201
DOI10.1137/15M1017119zbMath1342.62061arXiv1503.00021OpenAlexW2964029376MaRDI QIDQ5741201
Youssef M. Marzouk, Alex Gorodetsky
Publication date: 22 July 2016
Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1503.00021
polynomial approximationapproximation theorycomputer experimentsuncertainty quantificationexperimental designGaussian process regressionkernel interpolation
Nonparametric regression and quantile regression (62G08) Algorithms for approximation of functions (65D15)
Related Items
Clustered active-subspace based local Gaussian process emulator for high-dimensional and complex computer models ⋮ Bayesian Quadrature, Energy Minimization, and Space-Filling Design ⋮ Adaptive Gaussian Process Approximation for Bayesian Inference with Expensive Likelihood Functions ⋮ Cholesky-Based Experimental Design for Gaussian Process and Kernel-Based Emulation and Calibration ⋮ Locally induced Gaussian processes for large-scale simulation experiments ⋮ Gradient-based optimization for regression in the functional tensor-train format ⋮ Optimal Off-line Experimentation for Games ⋮ An Adaptive Minimum Spanning Tree Multielement Method for Uncertainty Quantification of Smooth and Discontinuous Responses
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Optimal designs for Gaussian process models via spectral decomposition
- Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids
- Sparse pseudospectral approximation method
- Stability of kernel-based interpolation
- Asymptotic analysis of stochastic programs
- The design and analysis of computer experiments.
- Dimension-adaptive tensor-product quadrature
- Design and analysis of computer experiments. With comments and a rejoinder by the authors
- Near-optimal data-independent point locations for radial basis function interpolation
- Positive integral operators in unbounded domains
- An extension of Mercer's theory to \(L^p\)
- High dimensional polynomial interpolation on sparse grids
- Batch sequential designs for computer experiments
- Spatial sampling design and covariance-robust minimax prediction based on convex design ideas
- Uncertainty Quantification given Discontinuous Model Response and a Limited Number of Model Runs
- Spectral Approximation of the IMSE Criterion for Optimal Designs in Kernel-Based Interpolation Models
- An Algorithm for the Construction of "D-Optimal" Experimental Designs
- Real Analysis and Probability
- An Exact Algorithm for Maximum Entropy Sampling
- Efficient Localization of Discontinuities in Complex Computational Simulations
- Mercer’s Theorem, Feature Maps, and Smoothing
- Adaptive Smolyak Pseudospectral Approximations
- Convergence of Unsymmetric Kernel‐Based Meshless Collocation Methods
- Sequential Design with Mutual Information for Computer Experiments (MICE): Emulation of a Tsunami Model
- On cardinal interpolation by Gaussian radial-basis functions: Properties of fundamental functions and estimates for Lebesgue constants