Gaussian processes with multidimensional distribution inputs via optimal transport and Hilbertian embedding

DOI10.1214/20-EJS1725zbMath1448.60085arXiv1805.00753MaRDI QIDQ2192319

Alexandra Suvorikova, François Bachoc, David Ginsbourger, Jean-Michel Loubes, Vladimir Spokoiny

Publication date: 17 August 2020

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.00753

zbMATH Keywords

kernel methodsWasserstein distanceHilbert space embeddings

Mathematics Subject Classification ID

Gaussian processes (60G15)

Related Items

On the use of Wasserstein distance in the distributional analysis of human decision making under uncertainty, Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measures, Gaussian field on the symmetric group: prediction and learning

Uses Software

• ElemStatLearn
• adagio
• Cast3M
• transport
• Barycenter

Cites Work

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• A fixed-point approach to barycenters in Wasserstein space
• Monge-Kantorovich depth, quantiles, ranks and signs
• Estimating the smoothness of a Gaussian random field from irregularly spaced data via higher-order quadratic variations
• Linear and nonlinear programming.
• Notes on the Wasserstein metric in Hilbert spaces
• Interpolation of spatial data. Some theory for kriging
• The design and analysis of computer experiments.
• On the continuity of center-outward distribution and quantile functions
• Computer experiments with functional inputs and scalar outputs by a norm-based approach
• Estimation and prediction using generalized Wendland covariance functions under fixed domain asymptotics
• Cross validation and maximum likelihood estimations of hyper-parameters of Gaussian processes with model misspecification
• Distribution's template estimate with Wasserstein metrics
• Sliced and Radon Wasserstein barycenters of measures
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• Existence and consistency of Wasserstein barycenters
• On the consistent separation of scale and variance for Gaussian random fields
• Asymptotic analysis of covariance parameter estimation for Gaussian processes in the misspecified case
• Barycenters in the Wasserstein Space
• Polar factorization and monotone rearrangement of vector‐valued functions
• Kernel Mean Embedding of Distributions: A Review and Beyond
• Characterization of barycenters in the Wasserstein space by averaging optimal transport maps
• A Gaussian Process Regression Model for Distribution Inputs
• Algorithmic Learning Theory
• Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics
• Optimal Transport
• Scattered Data Approximation