Cholesky-Based Experimental Design for Gaussian Process and Kernel-Based Emulation and Calibration (Communications in Computational Physics, 2021)
Gaussian processes and other kernel-based methods are used extensively toconstruct approximations of multivariate data sets. The accuracy of these approximations is dependent on the data used. This paper presents a computationally efficientalgorithm to greedily select training samples that minimize the weighted $L^p$ error ofkernel-based approximations for a given number of data. The method successivelygenerates nested samples, with the goal of minimizing the error in high probability regions of densities specified by users. The algorithm presented is extremely simple andcan be implemented using existing pivoted Cholesky factorization methods. Trainingsamples are generated in batches which allows training data to be evaluated (labeled)in parallel. For smooth kernels, the algorithm performs comparably with the greedyintegrated variance design but has significantly lower complexity. Numerical experiments demonstrate the efficacy of the approach for bounded, unbounded, multi-modaland non-tensor product densities. We also show how to use the proposed algorithmto efficiently generate surrogates for inferring unknown model parameters from datausing Bayesian inference.
Keywords: Experimental design; active learning; Gaussian process; radial basis function; uncertainty quantification; Bayesian inference.