Consistency of empirical Bayes and kernel flow for hierarchical parameter estimation

DOI10.1090/mcom/3649zbMath1472.62012arXiv2005.11375OpenAlexW3155546189MaRDI QIDQ4956916

Yi-Fan Chen, Houman Owhadi, Andrew M. Stuart

Publication date: 2 September 2021

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.11375

zbMATH Keywords

hierarchical parameter estimationprobabilistic Bayesian perspective

Mathematics Subject Classification ID

Gaussian processes (60G15) Point estimation (62F10) Bayesian problems; characterization of Bayes procedures (62C10) Interpolation in approximation theory (41A05) PDEs in connection with statistics (35Q62)

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Solving and learning nonlinear PDEs with Gaussian processes ⋮ Numerical methods for mean field games based on Gaussian processes and Fourier features ⋮ Computational graph completion ⋮ Learning dynamical systems from data: a simple cross-validation perspective. III: Irregularly-sampled time series ⋮ Asymptotic Bounds for Smoothness Parameter Estimates in Gaussian Process Interpolation ⋮ Gaussian process hydrodynamics ⋮ Kernel methods are competitive for operator learning ⋮ Learning ``best kernels from data in Gaussian process regression. With application to aerodynamics ⋮ Do ideas have shape? Idea registration as the continuous limit of artificial neural networks

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