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

Source: R/prediction.R
predict.Rd

[Updated]

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

Usage

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

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

# S3 method for class 'gp'
predict(
  object,
  x,
  method = NULL,
  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.

  • [Deprecated] if object is an instance of the lgp class created by lgp() without specifying argument struc in data frame form, x can be either a matrix or a list:

    • if x is a matrix, its rows are treated as instances of the Global inputs. In this case, it is assumed that the only global input to the system is the input to the emulators in the first layer and there is no global input to emulators in other layers.

    • if x is a list, it should have L (the number of layers in an emulator system) elements. The first element is a matrix that represents the global testing input data that feed into the emulators in the first layer of the system. The remaining L-1 elements are L-1 sub-lists, each of which contains a number (the same number of emulators in the corresponding layer) of matrices (rows being testing input data points and columns being input dimensions) that represent the global testing input data to the emulators in the corresponding layer. The matrices must be placed in the sub-lists based on how their corresponding emulators are placed in struc argument of lgp(). If there is no global input data to a certain emulator, set NULL in the corresponding sub-list of x.

    This option for linked (D)GP emulators is deprecated and will be removed in the next release.

  • [New] If object is an instance of the lgp class created by lgp() with argument struc in data frame form, 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. For DGP emulators with a categorical likelihood (likelihood = "Categorical" in dgp()), method is only applicable when full_layer = TRUE. In this case, the sampling approach generates samples from the GP nodes in all hidden layers using the derived means and variances, and subsequently propagates these samples through the categorical likelihood. By default, the method is set to "sampling" for DGP emulators with Poisson, Negative Binomial, and Categorical likelihoods, and to "mean_var" otherwise.

mode

[New] whether to predict the classes ("label") or probabilities ("proba") of different classes when object is a DGP emulator with a categorical likelihood. Defaults to "label".

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

[New] 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.

  • 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).

    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).

    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. 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().

    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. Each matrix gives samples of the output from one of D GP/likelihood nodes, and 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().

  • [New] If object is an instance of the dgp class with a categorical likelihood:

    1. if full_layer = FALSE and mode = "label": an updated object is returned with an additional slot called results that contains one matrix named label. The matrix has rows corresponding to testing positions and columns corresponding to sample labels of size: B * sample_size, where B is the number of imputations specified in dgp().

    2. if full_layer = FALSE and mode = "proba", an updated object is returned with an additional slot called results. This slot contains D matrices (where D is the number of classes in the training output), where each matrix gives probability samples for the corresponding class with its rows corresponding to testing positions and columns containing probabilities. The number of columns of each matrix is B * sample_size, where B is the number of imputations specified in the dgp() function.

    3. if method = "mean_var" 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 of first L-1 sub-lists contains two matrices named mean for the predictive means and var for the predictive variances of the GP nodes in the associated layer. Rows of each matrix correspond to testing positions.

      • when mode = "label", the sub-list LayerL contains one matrix named label. The matrix has its rows corresponding to testing positions and columns corresponding to label samples of size: B * sample_size. B is the number of imputations specified in dgp().

      • when mode = "proba", the sub-list LayerL contains D matrices (where D is the number of classes in the training output), where each matrix gives probability samples for the corresponding class with its rows corresponding to testing positions and columns containing probabilities. The number of columns of each matrix is B * sample_size. 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 of first L-1 sub-lists represents samples drawn from the GP nodes in the corresponding layer, and contains D (i.e., the number of GP nodes in the corresponding layer) matrices named output1, output2,..., outputD. Each matrix gives samples of the output from one of D GP nodes, and has its rows corresponding to testing positions and columns corresponding to samples of size: B * sample_size.

      • when mode = "label", the sub-list LayerL contains one matrix named label. The matrix has its rows corresponding to testing positions and columns corresponding to label samples of size: B * sample_size.

      • when mode = "proba", the sub-list LayerL contains D matrices (where D is the number of classes in the training output), where each matrix gives probability samples for the corresponding class with its rows corresponding to testing positions and columns containing probabilities. The number of columns of each matrix is B * sample_size.

      B is the number of imputations specified in dgp().

  • [Updated] 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().

    If object is an instance of the lgp class created by lgp() without specifying the struc argument in data frame form, the IDs, that are used as names of sub-lists or matrices within results, will be replaced by emulator1, emulator2, and so on.

The results slot will also include:

  • [New] 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.
} # }