deepgp-package: Package deepgp

In deepgp: Bayesian Deep Gaussian Processes using MCMC

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). Optional monotonic warpings are implemented following Barnett et al. (2024). 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, 32*(3), 824-837. 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

Barnett, S., Beesley, L. J., Booth, A. S., Gramacy, R. B., & Osthus D. (2024). Monotonic warpings for additive and deep Gaussian processes. *In Review.* arXiv:2408.01540

Examples

# See vignette, ?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/

deepgp documentation built on Sept. 11, 2024, 8:30 p.m.