Maintainer: Annie S. Booth annie_booth@ncsu.edu

Performs Bayesian posterior inference for deep Gaussian processes following Sauer, Gramacy, and Higdon (2023, ). See Sauer (2023, http://hdl.handle.net/10919/114845) 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 (2022, ). 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, 2021 ), and contour location through entropy (Sauer, 2023). 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. (2022). 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

What's new in version 1.1.1?

- Entropy calculations for contour locating sequential designs are offered through the specification of an
`entropy_limit`

in any of the`predict`

functions. - In posterior predictions, there is now an option to return point-wise mean and variance estimates for all MCMC samples through the specification of
`return_all = TRUE`

. - To save on memory and storage,
`predict`

functions no longer return`s2_smooth`

or`Sigma_smooth`

. If desired, these quantities may be calculated by subtracting`tau2*g`

from the diagonal. - The
`vecchia = TRUE`

option may now utilize either the Matern (`cov = "matern"`

) or squared exponential kernel (`cov = "exp2"`

"). - Performance improvements for
`cores = 1`

in`predict`

,`ALC`

, and`IMSE`

functions (helps to avoid a SNOW conflict when running multiple instances on the same machine). - Fit functions now return the outer log likelihood value along with MCMC samples. Used in trace plots to assess burn-in.
- In
`fit_two_layer`

, the intermediate latent layer may now have either a prior mean of zero (default) or a prior mean equal to`x`

(`pmx = TRUE`

). If`pmx`

is set to a constant, this will be the scale parameter on the inner Gaussian layer.

What's new in version 1.1.0?

- Package vignette
- Option to specify
`sep = TRUE`

in`fit_one_layer`

to fit a GP with separable/anisotropic lengthscales. - Default cores in predict are now 1 (this avoids a conflict when running multiple sessions simultaneously on a single machine).

What's new in version 1.0.1?

- Minor bug fixes/improvements.
- New warning message when OpenMP parallelization is not utilized for the Vecchia approximation. This happens when the package is downloaded from CRAN on a Mac. To set up OpenMP, download package source and compile with gcc/g++ instead of clang.

What's new in version 1.0.0?

- Models may now leverage the Vecchia approximation (through the specification of
`vecchia = TRUE`

in fit functions) for faster computation. The speed of this implementation relies on OpenMP parallelization (make sure the`-fopenmp`

flag is present with package installation). - SNOW parallelization now uses less memory/storage.
`tau2`

is now calculated at the time of MCMC, not at the time of prediction. This avoids some extra calculations.

What's new in version 0.3.0?

- The Matern kernel is now the default covariance. The smoothness parameter is user-adjustable but must be either
`v = 0.5`

,`v = 1.5`

, or`v = 2.5`

(default). The squared exponential kernel is still required for use with ALC and IMSE (set`cov = "exp2"`

in fit functions). - Expected improvement (EI) may now be computed concurrently with predictions. Set
`EI = TRUE`

inside`predict`

calls. EI calculations are nugget-free and are for*minimizing*the response (negate`y`

if maximization is desired). - To save memory, hidden layer mappings used in predictions are no longer stored and returned by default. To store them, set
`store_latent = TRUE`

inside predict.

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