deepgp-package {deepgp}R Documentation

Package deepgp

Description

Performs posterior inference for deep Gaussian processes following Sauer, Gramacy, and Higdon (2020) <arXiv:2012.08015>. 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 (2022) <arXiv:2204.02904>. Downstream tasks include sequential design through active learning Cohn/integrated mean squared error (ALC/IMSE; Sauer, Gramacy, and Higdon, 2020) and optimization through expected improvement (EI; Gramacy, Sauer, and Wycoff, 2021 <arXiv:2112.07457>). Models extend up to three layers deep; a one layer model is equivalent to typical Gaussian process regression. Covariance kernel options are matern (default) and squared exponential. Applicable to both noisy and deterministic functions. Incorporates SNOW parallelization and utilizes C and C++ under the hood.

Important Functions

Author(s)

Annie Sauer anniees@vt.edu

References

Sauer, A, RB Gramacy, and D Higdon. 2021. "Active Learning for Deep Gaussian Process Surrogates." Technometrics, (just-accepted), 1-39.

Sauer, A, A Cooper, and RB Gramacy. 2022. "Vecchia-approximated Deep Gaussian Processes for Computer Experiments." pre-print on arXiv:2204.02904

Katzfuss, M, J Guinness, W Gong, and D Zilber. 2020. "Vecchia aproximations of Gaussian-process predictions." Journal of Agricultural, Biological, and Environmental Statistics 25, 383-414.

Binois, M, J Huang, RB Gramacy, and M Ludkovski. 2019. Replication or Exploration? Sequential Design for Stochastic Simulation Experiments. Technometrics 61, 7-23. Taylor & Francis. doi:10.1080/00401706.2018.1469433.

Gramacy, RB. Surrogates: Gaussian Process Modeling, Design, and Optimization for the Applied Sciences. Chapman Hall, 2020.

Jones, DR, M Schonlau, and WJ Welch. 1998. "Efficient Global Optimization of Expensive Black-Box Functions." Journal of Global Optimization 13, 455-492. doi:10.1023/A:1008306431147.

Murray, I, RP Adams, and D MacKay. 2010. "Elliptical slice sampling." Journal of Machine Learning Research 9, 541-548.

Seo, S, M Wallat, T Graepel, and K Obermayer. 2000. Gaussian Process Regression: Active Data Selection and Test Point Rejection. In Mustererkennung 2000, 27-34. New York, NY: Springer Verlag.

Examples

# See "fit_one_layer", "fit_two_layer", "fit_three_layer", 
# "ALC", or "IMSE" for examples
# Examples of real-world implementations are available at: 
# https://bitbucket.org/gramacylab/deepgp-ex/


[Package deepgp version 1.0.0 Index]