deepgp Package

Maintainer: Annie S. Booth (

Performs Bayesian posterior inference for deep Gaussian processes following Sauer, Gramacy, and Higdon (2023). See Sauer (2023) for comprehensive methodological details and for a variety of coding examples. Models are trained through MCMC including elliptical slice sampling of latent Gaussian layers and Metropolis-Hastings sampling of kernel hyperparameters. Vecchia-approximation for faster computation is implemented following Sauer, Cooper, and Gramacy (2023). Downstream tasks include sequential design through active learning Cohn/integrated mean squared error (ALC/IMSE; Sauer, Gramacy, and Higdon, 2023), optimization through expected improvement (EI; Gramacy, Sauer, and Wycoff, 2022), and contour location through entropy (Booth, Renganathan, and Gramacy, 2024). Models extend up to three layers deep; a one layer model is equivalent to typical Gaussian process regression. Incorporates OpenMP and SNOW parallelization and utilizes C/C++ under the hood.

Run help("deepgp-package") or help(package = "deepgp") for more information.


Sauer, A. (2023). Deep Gaussian process surrogates for computer experiments. Ph.D. Dissertation, Department of Statistics, Virginia Polytechnic Institute and State University.

Sauer, A., Gramacy, R.B., & Higdon, D. (2023). Active learning for deep Gaussian process surrogates. Technometrics, 65, 4-18. arXiv:2012.08015

Sauer, A., Cooper, A., & Gramacy, R. B. (2023). Vecchia-approximated deep Gaussian processes for computer experiments. Journal of Computational and Graphical Statistics, 1-14. arXiv:2204.02904

Gramacy, R. B., Sauer, A. & Wycoff, N. (2022). Triangulation candidates for Bayesian optimization. Advances in Neural Information Processing Systems (NeurIPS), 35, 35933-35945. arXiv:2112.07457

Booth, A., Renganathan, S. A. & Gramacy, R. B. (2024). Contour location for reliability in airfoil simulation experiments using deep Gaussian processes. In Review. arXiv:2308.04420

Version History

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