TY - JOUR
T1 - Cholesky-Based Experimental Design for Gaussian Process and Kernel-Based Emulation and Calibration
AU - Harbrecht , Helumt
AU - D. Jakeman , John
AU - Zaspel , Peter
JO - Communications in Computational Physics
VL - 4
SP - 1152
EP - 1185
PY - 2021
DA - 2021/02
SN - 29
DO - http://doi.org/10.4208/cicp.OA-2020-0060
UR - https://global-sci.org/intro/article_detail/cicp/18644.html
KW - Experimental design, active learning, Gaussian process, radial basis function, uncertainty quantification, Bayesian inference.
AB - <p style="text-align: justify;">Gaussian processes and other kernel-based methods are used extensively to
construct approximations of multivariate data sets. The accuracy of these approximations is dependent on the data used. This paper presents a computationally efficient
algorithm to greedily select training samples that minimize the weighted $L^p$ error of
kernel-based approximations for a given number of data. The method successively
generates nested samples, with the goal of minimizing the error in high probability regions of densities specified by users. The algorithm presented is extremely simple and
can be implemented using existing pivoted Cholesky factorization methods. Training
samples are generated in batches which allows training data to be evaluated (labeled)
in parallel. For smooth kernels, the algorithm performs comparably with the greedy
integrated variance design but has significantly lower complexity. Numerical experiments demonstrate the efficacy of the approach for bounded, unbounded, multi-modal
and non-tensor product densities. We also show how to use the proposed algorithm
to efficiently generate surrogates for inferring unknown model parameters from data
using Bayesian inference.</p>