Locate the next design point for a (D)GP emulator or a bundle of (D)GP emulators using MICE

This function searches from a candidate set to locate the next design point(s) to be added to a (D)GP emulator or a bundle of (D)GP emulators using the Mutual Information for Computer Experiments (MICE), see the reference below.

Usage

mice(object, ...)

# S3 method for class 'gp'
mice(
  object,
  x_cand = NULL,
  n_cand = 200,
  batch_size = 1,
  M = 50,
  nugget_s = 1e-06,
  workers = 1,
  limits = NULL,
  int = FALSE,
  ...
)

# S3 method for class 'dgp'
mice(
  object,
  x_cand = NULL,
  n_cand = 200,
  batch_size = 1,
  M = 50,
  nugget_s = 1e-06,
  workers = 1,
  limits = NULL,
  int = FALSE,
  aggregate = NULL,
  ...
)

# S3 method for class 'bundle'
mice(
  object,
  x_cand = NULL,
  n_cand = 200,
  batch_size = 1,
  M = 50,
  nugget_s = 1e-06,
  workers = 1,
  limits = NULL,
  int = FALSE,
  aggregate = NULL,
  ...
)

Arguments

object

can be one of the following:

the S3 class gp.
the S3 class dgp.
the S3 class bundle.

...

any arguments (with names different from those of arguments used in mice()) that are used by aggregate can be passed here.

x_cand

a matrix (with each row being a design point and column being an input dimension) that gives a candidate set from which the next design point(s) are determined. If object is an instance of the bundle class and aggregate is not supplied, x_cand can also be a list. The list must have a length equal to the number of emulators in object, with each element being a matrix representing the candidate set for a corresponding emulator in the bundle. Defaults to NULL.

n_cand

an integer specifying the size of the candidate set to be generated for selecting the next design point(s). This argument is used only when x_cand is NULL. Defaults to 200.

batch_size

an integer that gives the number of design points to be chosen. Defaults to 1.

M

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

nugget_s

the value of the smoothing nugget term used by MICE. Defaults to 1e-6.

workers

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

limits

a two-column matrix that gives the ranges of each input dimension, or a vector of length two if there is only one input dimension. If a vector is provided, it will be converted to a two-column row matrix. The rows of the matrix correspond to input dimensions, and its first and second columns correspond to the minimum and maximum values of the input dimensions. This argument is only used when x_cand = NULL. Defaults to NULL.

int

a bool or a vector of bools that indicates if an input dimension is an integer type. If a single bool is given, it will be applied to all input dimensions. If a vector is provided, it should have a length equal to the input dimensions and will be applied to individual input dimensions. This argument is only used when x_cand = NULL. Defaults to FALSE.

aggregate

an R function that aggregates scores of the MICE across different output dimensions (if object is an instance of the dgp class) or across different emulators (if object is an instance of the bundle class). The function should be specified in the following basic form:

the first argument is a matrix representing scores. The rows of the matrix correspond to different design points. The number of columns of the matrix equals to:
- the emulator output dimension if object is an instance of the dgp class; or
- the number of emulators contained in object if object is an instance of the bundle class.
the output should be a vector that gives aggregate scores at different design points.

Set to NULL to disable aggregation. Defaults to NULL.

Value

If x_cand is not NULL:
- When object is an instance of the gp class, a vector of length batch_size is returned, containing the positions (row numbers) of the next design points from x_cand.
- When object is an instance of the dgp class, a vector of length batch_size * D is returned, containing the positions (row numbers) of the next design points from x_cand to be added to the DGP emulator.
  - D is the number of output dimensions of the DGP emulator if no likelihood layer is included.
  - For a DGP emulator with a Hetero or NegBin likelihood layer, D = 2.
  - For a DGP emulator with a Categorical likelihood layer, D = 1 for binary output or D = K for multi-class output with K classes.
- When object is an instance of the bundle class, a matrix is returned with batch_size rows and a column for each emulator in the bundle, containing the positions (row numbers) of the next design points from x_cand for individual emulators.
If x_cand is NULL:
- When object is an instance of the gp class, a matrix with batch_size rows is returned, giving the next design points to be evaluated.
- When object is an instance of the dgp class, a matrix with batch_size * D rows is returned, where:
  - D is the number of output dimensions of the DGP emulator if no likelihood layer is included.
  - For a DGP emulator with a Hetero or NegBin likelihood layer, D = 2.
  - For a DGP emulator with a Categorical likelihood layer, D = 1 for binary output or D = K for multi-class output with K classes.
- When object is an instance of the bundle class, a list is returned with a length equal to the number of emulators in the bundle. Each element of the list is a matrix with batch_size rows, where each row represents a design point to be added to the corresponding emulator.

Details

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

Note

The first column of the matrix supplied to the first argument of aggregate must correspond to the first output dimension of the DGP emulator if object is an instance of the dgp class, and so on for subsequent columns and dimensions. If object is an instance of the bundle class, the first column must correspond to the first emulator in the bundle, and so on for subsequent columns and emulators.

References

Beck, J., & Guillas, S. (2016). Sequential design with mutual information for computer experiments (MICE): emulation of a tsunami model. SIAM/ASA Journal on Uncertainty Quantification, 4(1), 739-766.

Examples

if (FALSE) { # \dontrun{

# load packages and the Python env
library(lhs)
library(dgpsi)

# construct a 1D non-stationary function
f <- function(x) {
 sin(30*((2*x-1)/2-0.4)^5)*cos(20*((2*x-1)/2-0.4))
}

# generate the initial design
X <- maximinLHS(10,1)
Y <- f(X)

# training a 2-layered DGP emulator with the global connection off
m <- dgp(X, Y, connect = F)

# generate a candidate set
x_cand <- maximinLHS(200,1)

# locate the next design point using MICE
next_point <- mice(m, x_cand = x_cand)
X_new <- x_cand[next_point,,drop = F]

# obtain the corresponding output at the located design point
Y_new <- f(X_new)

# combine the new input-output pair to the existing data
X <- rbind(X, X_new)
Y <- rbind(Y, Y_new)

# update the DGP emulator with the new input and output data and refit
m <- update(m, X, Y, refit = TRUE)

# plot the LOO validation
plot(m)
} # }