# deepgp Package

Maintainer: Annie S. Booth (<annie_booth@vt.edu>)

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.  Gradient-enhancement and gradient
predictions are offered following Booth (2026).  Vecchia approximation for faster 
computation is implemented following Sauer, Cooper, and Gramacy 
(2023).  Optional monotonic warpings are implemented following 
Barnett et al. (2025).  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, 
2025).  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.

## 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>

Booth, A. S. (2026). Gradient-enhancement and gradient predictions for deep 
Gaussian process modeling of expensive computer experiments. arXiv:2512.18066

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. (2025). Contour location for 
reliability in airfoil simulation experiments using deep Gaussian 
processes. *Annals of Applied Statistics, 19*(1), 191-211. arXiv:2308.04420

Barnett, S., Beesley, L. J., Booth, A. S., Gramacy, R. B., & Osthus D. (2025). 
Monotonic warpings for additive and deep Gaussian processes. 
*Statistics and Computing, 35*(3), 65. arXiv:2408.01540

## Version History

What's new in version 1.2.3?

* Minor bug fix when the package is installed without OpenMP

What's new in version 1.2.2?

* Gradient features (enhancement and predictions) now support `cov = "matern"` with `v = 2.5`
* Bug fix for `predict` with one-layer GP when `return_all = TRUE` and `cores = 1`.
Thanks Steven Barnett!

What's new in version 1.2.1?

* Replaced `span` with `arma::span` throughout C++ code to avoid namespace conflict
when compiled with `g++15` in `C++20` mode.
* Reduced the computation time required to compile the vignette by lowering the
number of MCMC samples used in each illustrative example.

What's new in version 1.2.0?

* Gradients!  All gradient implementations come with optional Vecchia approximation.
  + Gradient-enhancement is enabled through the `dydx` argument in `fit_one_layer` and
  `fit_two_layer` (gradient-enhancement is not yet offered for three layer models).
  Gradient-enhancement requires the `exp2` kernel.
  + Setting `grad = TRUE` in the `predict` or `post_sample` functions will return 
  posterior predictions/samples
  of the gradient (one and two layer only).  Again, this requires the `exp2` kernel.
* A new `post_sample` function offers joint posterior draws with optional Vecchia approximation 
  (compared to the `predict` functions that return summarized posterior moments).
* A new `to_vec` function will convert a non-Vecchia fit to a Vecchia approximated fit. 
  This is helpful when training data sizes are relatively small (not requiring Vecchia)
  but testing data sizes are large (requiring Vecchia).
* Additional user controls.
  + The user may now specify the scale (`tau2_w` and/or `tau2_z`) value to use on latent layers using
  the `settings` argument in `fit_two_layer` and `fit_three_layer`. 
  + The user may now specify the number of cores to use for Vecchia OpenMP parallelization using
  the optional `cores` argument in any of the fit functions.  If not specified, this defaults 
  to `min(4, maxcores - 1)`.
* Monotonic warpings are no longer scaled to [0, 1], and they now use an isotropic 
  lengthscale on the outer layer.
* Internal code improvements (external interface is unchanged):
  + Vecchia approximation objects and implementation have been streamlined.
  + The ordering of covariance parameters as arguments to internal functions has been 
  unified.  They are now always presented in the order: `tau2`, `theta`, `g`, `v`.
  + * If `true_g` is specified, the returned fit object no longer stores an entire
  vector of `g` values.  The specified `g` value is only stored once.
* User-specified hyperparameter priors are now set using a list with the 
  parameter name first, e.g.,
  `settings = list(theta = list(alpha = 1, beta = 1), g = list(alpha = 1, beta = 1))`.
* New warning message if `cores` used for SNOW parallelization is greater than the 
  number of provided `nmcmc` iterations.  If so, `cores` is overwritten with `cores = nmcmc`.
* Minor bug fix for use of `rand_mvn_vec` function when `pmx = TRUE` and the scale on
  the latent layer was not equal to 1.
* Bug fix for storage of `tau2` values within Gibbs sampling. Thanks Parul Patil!

What's new in version 1.1.3?

* Option to force monotonic warpings in the two-layer DGP with the argument 
  `monowarp = TRUE` to `fit_two_layer`.  Monotonic warpings trigger separable 
  lengthscales on the outer layer.
* Updated default prior values on lengthscales and nugget for noisy settings 
  (when `true_g = NULL`)
* Minor bug fix in Gibbs updating of separable lengthscale sampling in 
  `fit_one_layer`
* Some improvements to default plotting
* Updated package examples and vignette

What's new in version 1.1.2?

* Option for user to specify ordering for Vecchia approximation 
  (through `ord` argument in `fit` functions)
* `lite = TRUE` predictions have been sped up
  + bypassing the `cov(t(mu_t))` computation altogether (this is only necessary 
    for `lite = FALSE`)
  + removing `d_new` calculations 
  + using `diag_quad_mat` Cpp function more often 
* Expected improvement is now available for Vecchia-approximated fits
* Internally, predict functions have been consolidated (removing hundreds of
  lines of redundant code)
* Removed internal `clean_prediction` function as it was no longer needed
* Minor bug fixes
  + Fixed error in `fit_one_layer` with `vecchia = TRUE` and `sep = TRUE` caused 
    by the `arma::mat covmat` initialization in the `vecchia.cpp` file
  + Fixed error in `predict.dgp2` with `return_all = TRUE` (replaced `out` with 
    `object` - thanks Steven Barnett!)
  + Fixed storage of `ll` in `continue` functions (thanks Sebastien Coube!)

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.


