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Prediction from GP, DGP, or linked (D)GP emulators

Source: R/prediction.R
predict.Rd

This function implements prediction from GP, DGP, or linked (D)GP emulators.

Usage

# S3 method for class 'dgp'
predict(
  object,
  x,
  method = "mean_var",
  full_layer = FALSE,
  sample_size = 50,
  M = 50,
  cores = 1,
  chunks = NULL,
  ...
)

# S3 method for class 'lgp'
predict(
  object,
  x,
  method = "mean_var",
  full_layer = FALSE,
  sample_size = 50,
  M = 50,
  cores = 1,
  chunks = NULL,
  ...
)

# S3 method for class 'gp'
predict(
  object,
  x,
  method = "mean_var",
  sample_size = 50,
  M = 50,
  cores = 1,
  chunks = NULL,
  ...
)

Arguments

object

an instance of the gp, dgp, or lgp class.

x

the testing input data:

  • if object is an instance of the gp or dgp class, x is a matrix where each row is an input testing data point and each column is an input dimension.

  • if object is an instance of the lgp class, x must be a matrix representing the global input, where each row corresponds to a test data point and each column represents a global input dimension. The column indices in x must align with the indices specified in the From_Output column of the struc data frame (used in lgp()), corresponding to rows where the From_Emulator column is "Global".

method

[Updated] the prediction approach to use: either the mean-variance approach ("mean_var") or the sampling approach ("sampling"). The mean-variance approach returns the means and variances of the predictive distributions, while the sampling approach generates samples from predictive distributions using the derived means and variances. Defaults to "mean_var".

full_layer

a bool indicating whether to output the predictions of all layers. Defaults to FALSE. Only used when object is a DGP or a linked (D)GP emulator.

sample_size

the number of samples to draw for each given imputation if method = "sampling". Defaults to 50.

M

the size of the conditioning set for the Vecchia approximation in the emulator prediction. Defaults to 50. This argument is only used if the emulator object was constructed under the Vecchia approximation.

cores

the number of processes to be used for prediction. If set to NULL, the number of processes is set to max physical cores available %/% 2. Defaults to 1.

chunks

the number of chunks that the testing input matrix x will be divided into for multi-cores to work on. Only used when cores is not 1. If not specified (i.e., chunks = NULL), the number of chunks is set to the value of cores. Defaults to NULL.

...

N/A.

Value

  • If object is an instance of the gp class:

    1. if method = "mean_var": an updated object is returned with an additional slot called results that contains two matrices named mean for the predictive means and var for the predictive variances. Each matrix has only one column with its rows corresponding to testing positions (i.e., rows of x).

    2. if method = "sampling": an updated object is returned with an additional slot called results that contains a matrix whose rows correspond to testing positions and columns correspond to sample_size number of samples drawn from the predictive distribution of GP.

  • [Updated] If object is an instance of the dgp class:

    1. if method = "mean_var" and full_layer = FALSE: an updated object is returned with an additional slot called results that contains two matrices named mean for the predictive means and var for the predictive variances respectively. Each matrix has its rows corresponding to testing positions and columns corresponding to DGP global output dimensions (i.e., the number of GP/likelihood nodes in the final layer). If the likelihood node is categorical, the matrices contain the predictive means and variances of the class probabilities, with columns corresponding to different classes.

    2. if method = "mean_var" and full_layer = TRUE: an updated object is returned with an additional slot called results that contains two sub-lists named mean for the predictive means and var for the predictive variances respectively. Each sub-list contains L (i.e., the number of layers) matrices named layer1, layer2,..., layerL. Each matrix has its rows corresponding to testing positions and columns corresponding to output dimensions (i.e., the number of GP/likelihood nodes from the associated layer). If the likelihood node is categorical, the matrices named layerL in both mean and var contain the predictive means and variances of the class probabilities, respectively, with columns corresponding to different classes.

    3. if method = "sampling" and full_layer = FALSE: an updated object is returned with an additional slot called results that contains D (i.e., the number of GP/likelihood nodes in the final layer) matrices named output1, output2,..., outputD. If the likelihood node in the final layer is categorical, results contains D matrices (where D is the number of classes) of sampled class probabilities, each named according to its corresponding class label. Each matrix in results has its rows corresponding to testing positions and columns corresponding to samples of size: B * sample_size, where B is the number of imputations specified in dgp().

    4. if method = "sampling" and full_layer = TRUE: an updated object is returned with an additional slot called results that contains L (i.e., the number of layers) sub-lists named layer1, layer2,..., layerL. Each sub-list represents samples drawn from the GP/likelihood nodes in the corresponding layer, and contains D (i.e., the number of GP/likelihood nodes in the corresponding layer) matrices named output1, output2,..., outputD. If the likelihood node in the final layer is categorical, layerL contains D matrices (where D is the number of classes) of sampled class probabilities, each named according to its corresponding class label. Each matrix has its rows corresponding to testing positions and columns corresponding to samples of size: B * sample_size, where B is the number of imputations specified in dgp().

  • If object is an instance of the lgp class:

    1. if method = "mean_var" and full_layer = FALSE: an updated object is returned with an additional slot called results that contains two sub-lists named mean for the predictive means and var for the predictive variances respectively. Each sub-list contains K (same number of emulators in the final layer of the system) matrices named using the IDs of the corresponding emulators in the final layer. Each matrix has rows corresponding to global testing positions and columns corresponding to output dimensions of the associated emulator in the final layer.

    2. if method = "mean_var" and full_layer = TRUE: an updated object is returned with an additional slot called results that contains two sub-lists named mean for the predictive means and var for the predictive variances respectively. Each sub-list contains L (i.e., the number of layers in the emulated system) components named layer1, layer2,..., layerL. Each component represents a layer and contains K (same number of emulators in the corresponding layer of the system) matrices named using the IDs of the corresponding emulators in that layer. Each matrix has its rows corresponding to global testing positions and columns corresponding to output dimensions of the associated GP/DGP emulator in the corresponding layer.

    3. if method = "sampling" and full_layer = FALSE: an updated object is returned with an additional slot called results that contains K (same number of emulators in the final layer of the system) sub-lists named using the IDs of the corresponding emulators in the final layer. Each sub-list contains D matrices, named output1, output2,..., outputD, that correspond to the output dimensions of the GP/DGP emulator. Each matrix has rows corresponding to testing positions and columns corresponding to samples of size: B * sample_size, where B is the number of imputations specified in lgp().

    4. if method = "sampling" and full_layer = TRUE: an updated object is returned with an additional slot called results that contains L (i.e., the number of layers of the emulated system) sub-lists named layer1, layer2,..., layerL. Each sub-list represents a layer and contains K (same number of emulators in the corresponding layer of the system) components named using the IDs of the corresponding emulators in that layer. Each component contains D matrices, named output1, output2,..., outputD, that correspond to the output dimensions of the GP/DGP emulator. Each matrix has its rows corresponding to testing positions and columns corresponding to samples of size: B * sample_size, where B is the number of imputations specified in lgp().

The results slot will also include:

  • the value of M, which represents the size of the conditioning set for the Vecchia approximation, if used, in the emulator prediction.

  • the value of sample_size if method = "sampling".

Details

See further examples and tutorials at https://mingdeyu.github.io/dgpsi-R/.

Examples

if (FALSE) { # \dontrun{

# See gp(), dgp(), or lgp() for an example.
} # }