predict: Predict posterior mean and variance/covariance

In deepgp: Deep Gaussian Processes using MCMC

Predict posterior mean and variance/covariance

Description

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

Usage

## S3 method for class 'gp'
predict(object, x_new, lite = TRUE, EI = FALSE, cores = 1, ...)

## S3 method for class 'dgp2'
predict(
  object,
  x_new,
  lite = TRUE,
  store_latent = FALSE,
  mean_map = TRUE,
  EI = FALSE,
  cores = 1,
  ...
)

## S3 method for class 'dgp3'
predict(
  object,
  x_new,
  lite = TRUE,
  store_latent = FALSE,
  mean_map = TRUE,
  EI = FALSE,
  cores = 1,
  ...
)

## S3 method for class 'gpvec'
predict(object, x_new, m = object$m, lite = TRUE, cores = 1, ...)

## S3 method for class 'dgp2vec'
predict(
  object,
  x_new,
  m = object$m,
  lite = TRUE,
  store_latent = FALSE,
  mean_map = TRUE,
  cores = 1,
  ...
)

## S3 method for class 'dgp3vec'
predict(
  object,
  x_new,
  m = object$m,
  lite = TRUE,
  store_latent = FALSE,
  mean_map = TRUE,
  cores = 1,
  ...
)

Arguments

object	object from fit_one_layer, fit_two_layer, or fit_three_layer with burn-in already removed
x_new	matrix of predictive input locations
lite	logical indicating whether to calculate only point-wise variances (lite = TRUE) or full covariance (lite = FALSE)
EI	logical indicating whether to calculate expected improvement (for minimizing the response)
cores	number of cores to utilize in parallel, defaults to available cores minus one
...	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), mean_map = FALSE is not yet implemented for fits with vecchia = TRUE
m	size of Vecchia conditioning sets (only for fits with vecchia = TRUE), defaults to the m used for MCMC

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.

SNOW parallelization reduces computation time but requires more memory storage.

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)

• s2_smooth: predicted point-wise variances with g removed, indices correspond to x_new locations (only returned when lite = TRUE)

• Sigma: predicted posterior covariance, indices correspond to x_new locations (only returned when lite = FALSE)

• Sigma_smooth: predicted posterior covariance with g removed from the diagonal (only returned when lite = FALSE)

• EI: vector of expected improvement values, indices correspond to x_new locations (only returned when EI = TRUE)

• w_new: list of hidden layer mappings (only returned when store_latent = TRUE), list index corresponds to iteration and row index corresponds to x_new location (two or three layer models only)

• z_new: list of hidden layer mappings (only returned when store_latent = TRUE), list index corresponds to iteration and row index corresponds to x_new location (three layer models only)

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

References

Sauer, A, RB Gramacy, and D Higdon. 2020. "Active Learning for Deep Gaussian Process Surrogates." Technometrics, to appear; arXiv:2012.08015.

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

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

Examples

# See "fit_one_layer", "fit_two_layer", or "fit_three_layer"
# for an example

deepgp documentation built on Dec. 28, 2022, 1:32 a.m.