deepgp-package {deepgp}

Package deepgp

Description

Performs Bayesian posterior inference for deep Gaussian processes following Sauer, Gramacy, and Higdon (2023). See Sauer (2023) for comprehensive methodological details and https://bitbucket.org/gramacylab/deepgp-ex/ 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.

Important Functions

• fit_one_layer: conducts MCMC sampling of hyperparameters for a one layer GP

• fit_two_layer: conducts MCMC sampling of hyperparameters and hidden layer for a two layer deep GP

• fit_three_layer: conducts MCMC sampling of hyperparameters and hidden layers for a three layer deep GP

• continue: collects additional MCMC samples

• trim: cuts off burn-in and optionally thins samples

• predict: calculates posterior mean and variance over a set of input locations (optionally calculates EI or entropy)

• plot: produces trace plots, hidden layer plots, and posterior predictive plots

• ALC: calculates active learning Cohn over set of input locations using reference grid

• IMSE: calculates integrated mean-squared error over set of input locations

Author(s)

Annie S. Booth [e-mail]

References

Sauer, A. (2023). Deep Gaussian process surrogates for computer experiments. *Ph.D. Dissertation, Department of Statistics, Virginia Polytechnic Institute and State University.* http://hdl.handle.net/10919/114845

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

Examples

# See "fit_one_layer", "fit_two_layer", "fit_three_layer", 
# "ALC", or "IMSE" for examples
# Many more examples including real-world computer experiments are available at: 
# https://bitbucket.org/gramacylab/deepgp-ex/