predict: Predict posterior mean and variance/covariance

Description

Acts on a gp, gpvec, dgp2, dgp2vec, dgp3, or dgp3vec object. Calculates posterior mean and variance/covariance over specified input locations. Optionally calculates expected improvement (EI) or entropy over candidate inputs. Optionally utilizes SNOW parallelization.

Usage

# S3 method for gp
predict(
  object,
  x_new,
  lite = TRUE,
  grad = FALSE,
  return_all = FALSE,
  EI = FALSE,
  entropy_limit = NULL,
  cores = 1,
  ...
)
# S3 method for dgp2
predict(
  object,
  x_new,
  lite = TRUE,
  grad = FALSE,
  store_latent = FALSE,
  mean_map = TRUE,
  return_all = FALSE,
  EI = FALSE,
  entropy_limit = NULL,
  cores = 1,
  ...
)
# S3 method for dgp3
predict(
  object,
  x_new,
  lite = TRUE,
  store_latent = FALSE,
  mean_map = TRUE,
  return_all = FALSE,
  EI = FALSE,
  entropy_limit = NULL,
  cores = 1,
  ...
)
# S3 method for gpvec
predict(
  object,
  x_new,
  m = NULL,
  ord_new = NULL,
  lite = TRUE,
  grad = FALSE,
  return_all = FALSE,
  EI = FALSE,
  entropy_limit = NULL,
  cores = 1,
  ...
)
# S3 method for dgp2vec
predict(
  object,
  x_new,
  m = NULL,
  ord_new = NULL,
  lite = TRUE,
  grad = FALSE,
  store_latent = FALSE,
  mean_map = TRUE,
  return_all = FALSE,
  EI = FALSE,
  entropy_limit = NULL,
  cores = 1,
  ...
)
# S3 method for dgp3vec
predict(
  object,
  x_new,
  m = NULL,
  ord_new = NULL,
  lite = TRUE,
  store_latent = FALSE,
  mean_map = TRUE,
  return_all = FALSE,
  EI = FALSE,
  entropy_limit = NULL,
  cores = 1,
  ...
)

Value

object of the same class with the following additional elements:

x_new: copy of predictive input locations
mean: predicted posterior mean, indices correspond to x_new locations
s2: predicted point-wise variances, indices correspond to x_new locations (only returned when lite = TRUE)
mean_all: predicted posterior mean for each sample (rows correspond to iterations), only returned when return_all = TRUE
s2_all: predicted point-wise variances for each sample (rows correspond to iterations), only returned when return_all = TRUE
Sigma: predicted posterior covariance, indices correspond to x_new locations (only returned when lite = FALSE)
grad_mean: predicted posterior mean of the gradient (rows correspond to x_new, columns correspond to dimension, only returned when grad = TRUE)
grad_s2: predicted point-wise variances of the gradient (rows correspond to x_new, columns correspond to dimension, only returned when grad = TRUE)
EI: vector of expected improvement values, indices correspond to x_new locations (only returned when EI = TRUE)
entropy: vector of entropy values, indices correspond to x_new locations (only returned when entropy_limit is numeric)
w_new: array of hidden layer mappings, with dimensions corresponding to iteration, then x_new location, then dimension (only returned when store_latent = TRUE)
z_new: array of hidden layer mappings, with dimensions corresponding to iteration, then x_new location, then dimension (only returned when store_latent = TRUE)

Computation time is added to the computation time of the existing object.

Arguments

object: object from fit_one_layer, fit_two_layer, or fit_three_layer with burn-in already removed
x_new: vector or matrix of predictive input locations
lite: logical indicating whether to calculate only point-wise variances (lite = TRUE) or full covariance (lite = FALSE)
grad: logical indicating whether to additionally calculate/return predictions of the gradient (one and two layer models only)
return_all: logical indicating whether to return mean and point-wise variance prediction for ALL samples (only available for lite = TRUE)
EI: logical indicating whether to calculate expected improvement (for minimizing the response)
entropy_limit: optional limit state for entropy calculations (separating passes and failures), default value of NULL bypasses entropy calculations
cores: number of cores to utilize for SNOW parallelization
...: N/A
store_latent: logical indicating whether to store and return mapped values of latent layers (two or three layer models only)
mean_map: logical indicating whether to map hidden layers using conditional mean (mean_map = TRUE) or using a random sample from the full MVN distribution (two or three layer models only)
m: size of Vecchia conditioning sets, defaults to the lower of twice the m used for MCMC or the maximum available (only for fits with vecchia = TRUE),
ord_new: optional ordering for Vecchia approximation with lite = FALSE, must correspond to rows of x_new, defaults to random, is applied to all layers in deeper models

Details

All iterations in the object are used for prediction, so samples should be burned-in. Thinning the samples using trim will speed up computation. Posterior moments are calculated using conditional expectation and variance. As a default, only point-wise variance is calculated. Full covariance may be calculated using lite = FALSE.

Expected improvement is calculated with the goal of minimizing the response. See Chapter 7 of Gramacy (2020) for details. Entropy is calculated based on two classes separated by the specified limit. See Sauer (2023, Chapter 3) for details.

SNOW parallelization reduces computation time but requires more memory storage.

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. (2025). Deep Gaussian processes with gradients. 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

Examples

Run this code

# See ?fit_one_layer, ?fit_two_layer, or ?fit_three_layer
# for examples

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