validate: Validate a constructed GP, DGP, or linked (D)GP emulator

In dgpsi: Interface to 'dgpsi' for Deep and Linked Gaussian Process Emulations

Validate a constructed GP, DGP, or linked (D)GP emulator

Description

This function calculates Leave-One-Out (LOO) cross validation or Out-Of-Sample (OOS) validation statistics for a constructed GP, DGP, or linked (D)GP emulator.

Usage

validate(
  object,
  x_test,
  y_test,
  method,
  sample_size,
  verb,
  M,
  force,
  cores,
  ...
)

## S3 method for class 'gp'
validate(
  object,
  x_test = NULL,
  y_test = NULL,
  method = NULL,
  sample_size = 50,
  verb = TRUE,
  M = 50,
  force = FALSE,
  cores = 1,
  ...
)

## S3 method for class 'dgp'
validate(
  object,
  x_test = NULL,
  y_test = NULL,
  method = NULL,
  sample_size = 50,
  verb = TRUE,
  M = 50,
  force = FALSE,
  cores = 1,
  ...
)

## S3 method for class 'lgp'
validate(
  object,
  x_test = NULL,
  y_test = NULL,
  method = NULL,
  sample_size = 50,
  verb = TRUE,
  M = 50,
  force = FALSE,
  cores = 1,
  ...
)

Arguments

object	can be one of the following: the S3 class gp. the S3 class dgp. the S3 class lgp.
x_test	OOS testing input data: if object is an instance of the gp or dgp class, x_test is a matrix where each row is a new input location to be used for validating the emulator and each column is an input dimension. if object is an instance of the lgp class, x_test can be a matrix or a list: if x_test is a matrix, it is the global testing input data that feed into the emulators in the first layer of a system. The rows of x_test represent different input data points and the columns represent input dimensions across all emulators in the first layer of the system. 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_test 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_test. This option for linked (D)GP emulators is deprecated and will be removed in the next release. If object is an instance of the lgp class created by lgp() with argument struc in data frame form, x_test 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_test 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". x_test must be provided if object is an instance of the lgp. x_test must also be provided if y_test is provided. Defaults to NULL, in which case LOO validation is performed.
y_test	the OOS output data corresponding to x_test: if object is an instance of the gp class, y_test is a matrix with only one column where each row represents the output corresponding to the matching row of x_test. if object is an instance of the dgp class, y_test is a matrix where each row represents the output corresponding to the matching row of x_test and with columns representing output dimensions. if object is an instance of the lgp class, y_test can be a single matrix or a list of matrices: if y_test is a single matrix, then there should be only one emulator in the final layer of the linked emulator system and y_test represents the emulator's output with rows being testing positions and columns being output dimensions. if y_test is a list, then y_test should have L matrices, where L is the number of emulators in the final layer of the system. Each matrix has its rows corresponding to testing positions and columns corresponding to output dimensions of the associated emulator in the final layer. y_test must be provided if object is an instance of the lgp. y_test must also be provided if x_test is provided. Defaults to NULL, in which case LOO validation is performed.
method	the prediction approach to use for validation: either the mean-variance approach ("mean_var") or the sampling approach ("sampling"). For details see predict(). For DGP emulators with a categorical likelihood (likelihood = "Categorical" in dgp()), only the sampling approach is supported. By default, the method is set to "sampling" for DGP emulators with Poisson, Negative Binomial, and Categorical likelihoods and "mean_var" otherwise.
sample_size	the number of samples to draw for each given imputation if method = "sampling". Defaults to 50.
verb	a bool indicating if trace information for validation should be printed during function execution. Defaults to TRUE.
M	the size of the conditioning set for the Vecchia approximation in emulator validation. This argument is only used if the emulator object was constructed under the Vecchia approximation. Defaults to 50.
force	a bool indicating whether to force LOO or OOS re-evaluation when the loo or oos slot already exists in object. When force = FALSE, validate() will only re-evaluate the emulators if the x_test and y_test are not identical to the values in the oos slot. If the existing loo or oos validation used a different M in a Vecchia approximation or a different method to the one prescribed in this call, the emulator will be re-evaluated. Set force to TRUE when LOO or OOS re-evaluation is required. Defaults to FALSE.
cores	the number of processes to be used for validation. If set to NULL, the number of processes is set to ⁠max physical cores available %/% 2⁠. Defaults to 1.
...	N/A.

Details

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

Value

• If object is an instance of the gp class, an updated object is returned with an additional slot called loo (for LOO cross validation) or oos (for OOS validation) that contains:

  • two slots called x_train (or x_test) and y_train (or y_test) that contain the validation data points for LOO (or OOS).

  • a column matrix called mean, if method = "mean_var", or median, if method = "sampling", that contains the predictive means or medians of the GP emulator at validation positions.

  • three column matrices called std, lower, and upper that contain the predictive standard deviations and credible intervals of the GP emulator at validation positions. If method = "mean_var", the upper and lower bounds of a credible interval are two standard deviations above and below the predictive mean. If method = "sampling", the upper and lower bounds of a credible interval are 2.5th and 97.5th percentiles.

  • a numeric value called rmse that contains the root mean/median squared error of the GP emulator.

  • a numeric value called nrmse that contains the (max-min) normalized root mean/median squared error of the GP emulator. The max-min normalization uses the maximum and minimum values of the validation outputs contained in y_train (or y_test).

  • an integer called M that contains the size of the conditioning set used for the Vecchia approximation, if used, for emulator validation.

  • an integer called sample_size that contains the number of samples used for validation if method = "sampling".

  The rows of matrices (mean, median, std, lower, and upper) correspond to the validation positions.

• If object is an instance of the dgp class, an updated object is returned with an additional slot called loo (for LOO cross validation) or oos (for OOS validation) that contains:

  • two slots called x_train (or x_test) and y_train (or y_test) that contain the validation data points for LOO (or OOS).

  • a matrix called mean, if method = "mean_var", or median, if method = "sampling", that contains the predictive means or medians of the DGP emulator at validation positions.

  • three matrices called std, lower, and upper that contain the predictive standard deviations and credible intervals of the DGP emulator at validation positions. If method = "mean_var", the upper and lower bounds of a credible interval are two standard deviations above and below the predictive mean. If method = "sampling", the upper and lower bounds of a credible interval are 2.5th and 97.5th percentiles.

  • a vector called rmse that contains the root mean/median squared errors of the DGP emulator across different output dimensions.

  • a vector called nrmse that contains the (max-min) normalized root mean/median squared errors of the DGP emulator across different output dimensions. The max-min normalization uses the maximum and minimum values of the validation outputs contained in y_train (or y_test).

  • an integer called M that contains size of the conditioning set used for the Vecchia approximation, if used, for emulator validation.

  • an integer called sample_size that contains the number of samples used for validation if method = "sampling".

  The rows and columns of matrices (mean, median, std, lower, and upper) correspond to the validation positions and DGP emulator output dimensions, respectively.

• If object is an instance of the dgp class with a categorical likelihood, an updated object is returned with an additional slot called loo (for LOO cross validation) or oos (for OOS validation) that contains:

  • two slots called x_train (or x_test) and y_train (or y_test) that contain the validation data points for LOO (or OOS).

  • a matrix called label that contains predictive samples of labels from the DGP emulator at validation positions. The matrix has its rows corresponding to validation positions and columns corresponding to samples of labels.

  • a list called probability that contains predictive samples of probabilities for each class from the DGP emulator at validation positions. The element in the list is a matrix that has its rows corresponding to validation positions and columns corresponding to samples of probabilities.

  • a scalar called log_loss that represents the average log loss of the predicted labels in the DGP emulator across all validation positions. Log loss measures the accuracy of probabilistic predictions, with lower values indicating better classification performance. log_loss ranges from 0 to positive infinity, where a value closer to 0 suggests more confident and accurate predictions.

  • an integer called M that contains size of the conditioning set used for the Vecchia approximation, if used, in emulator validation.

  • an integer called sample_size that contains the number of samples used for validation.

• If object is an instance of the lgp class, an updated object is returned with an additional slot called oos (for OOS validation) that contains:

  • two slots called x_test and y_test that contain the validation data points for OOS.

  • a list called mean, if method = "mean_var", or median, if method = "sampling", that contains the predictive means or medians of the linked (D)GP emulator at validation positions.

  • three lists called std, lower, and upper that contain the predictive standard deviations and credible intervals of the linked (D)GP emulator at validation positions. If method = "mean_var", the upper and lower bounds of a credible interval are two standard deviations above and below the predictive mean. If method = "sampling", the upper and lower bounds of a credible interval are 2.5th and 97.5th percentiles.

  • a list called rmse that contains the root mean/median squared errors of the linked (D)GP emulator.

  • a list called nrmse that contains the (max-min) normalized root mean/median squared errors of the linked (D)GP emulator. The max-min normalization uses the maximum and minimum values of the validation outputs contained in y_test.

  • an integer called M that contains size of the conditioning set used for the Vecchia approximation, if used, in emulator validation.

  • an integer called sample_size that contains the number of samples used for validation if method = "sampling".

  Each element in mean, median, std, lower, upper, rmse, and nrmse corresponds to a (D)GP emulator in the final layer of the linked (D)GP emulator.

Note

• When both x_test and y_test are NULL, LOO cross validation will be implemented. Otherwise, OOS validation will be implemented. LOO validation is only applicable to a GP or DGP emulator (i.e., object is an instance of the gp or dgp class). If a linked (D)GP emulator (i.e., object is an instance of the lgp class) is provided, x_test and y_test must also be provided for OOS validation.

Examples

## Not run: 

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

## End(Not run)

dgpsi documentation built on April 3, 2025, 9:26 p.m.