update: Easy update of funGp funGp Gaussian process models

Description

This method enables the update of data or hyperparameters of a funGp Gaussian process model. It corresponds to an object of the class '>fgpm. The method allows addition, subtraction and substitution of data points, as well as substitution and re-estimation of hyperparameters.

Usage

update(object, ...)
# S4 method for fgpm
update(
  object,
  sIn.nw = NULL,
  fIn.nw = NULL,
  sOut.nw = NULL,
  sIn.sb = NULL,
  fIn.sb = NULL,
  sOut.sb = NULL,
  ind.sb = NULL,
  ind.dl = NULL,
  var.sb = NULL,
  ls_s.sb = NULL,
  ls_f.sb = NULL,
  var.re = FALSE,
  ls_s.re = FALSE,
  ls_f.re = FALSE,
  ...
)

Arguments

object

an object of class '>fgpm corresponding to the funGp model to update.

...

not used.

sIn.nw

an optional matrix of scalar input values to be added to the model. Each column must match an input variable and each row a scalar coordinate.

fIn.nw

an optional list of functional input values to be added to the model. Each element of the list must be a matrix containing to the set of curves corresponding to one functional input.

sOut.nw

an optional vector (or 1-column matrix) containing the values of the scalar output at the new input points.

sIn.sb

an optional matrix of scalar input values to be used as substitutes of other scalar input values already stored in the model. Each column must match an input variable and each row a coordinate.

fIn.sb

an optional list of functional input values to be added to the model. Each element of the list must be a matrix containing to the set of curves corresponding to one functional input.

sOut.sb

an optional vector (or 1-column matrix) containing the values of the scalar output at the substituting input points.

ind.sb

an optional numeric array indicating the indices of the input and output points stored in the model, that should be replaced by the values specified through sIn.sb, fIn.sb and/or, sOut.sb.

ind.dl

an optional numeric array indicating the indices of the input and output points stored in the model that should be deleted.

var.sb

an optional number indicating the value that should be used to substitute the current variance parameter of the model.

ls_s.sb

an optional numerical array indicating the values that should be used to substitute the current length-scale parameters for the scalar inputs of the model.

ls_f.sb

an optional numerical array indicating the values that should be used to substitute the current length-scale parameters for the functional inputs of the model.

var.re

an optional boolean indicating whether the variance parameter should be re-estimated. Default is FALSE.

ls_s.re

an optional boolean indicating whether the length-scale parameters of the scalar inputs should be re-estimated. Default is FALSE.

ls_f.re

an optional boolean indicating whether the length-scale parameters of the functional inputs should be re-estimated. Default is FALSE.

Value

An object of class '>fgpm representing the updated funGp model.

Details

The arguments listed above enable the completion of the following updating tasks:

Deletion of data points: ind.dl;
Addition of data points: sIn.nw, fIn.nw, sOut.nw;
Substitution of data points: sIn.sb, fIn.sb, sOut.sb, ind.sb;
Substitution of hyperparameters: var.sb, ls_s.sb, ls_f.sb;
Re-estimation of hyperparameters: var.re, ls_s.re, ls_f.re.

All the arguments listed above are optional since any of these tasks can be requested without need to request any of the other tasks. In fact, even most of the arguments can be used even if the other arguments related to the same task are not. For instance, the re-estimation of the variance can be requested via var.re without requiring re-estimation of the scalar or functional length-scale parameters. The only two exceptions are: (i) for data addition, the new output sOut.nw should always be provided and the new input points should correspond to the set of variables already stored in the '>fgpm object passed for update; and (ii) for data substitution, the argument ind.sb is always mandatory.

Conflicting task combinations:

Data points deletion and substitution;
Substitution and re-estimation of the same hyperparameter.

Note that the parameters of the model will not be updated after modifying the model unless explicitly requested through the var.re, ls_s.re and ls_f.re arguments. If, for instance, some points are added to the model without requesting parameters re-estimation, the new data will be included in the training-training and training-prediction covariance matrices, but the hyperparameters will not be updated. This allows to make updates in the data that might help to improve predictions, without the immediate need to perform a training procedure that could be time consuming. At any later time, the user is allowed to request the re-estimation of the hyperparameters, which will make the model be fully up to date.

Examples

Run this code

# NOT RUN {
# deletion and addition of data points_____________________________________________________
# building the model
set.seed(100)
n.tr <- 25
sIn <- expand.grid(x1 = seq(0,1,length = sqrt(n.tr)), x2 = seq(0,1,length = sqrt(n.tr)))
fIn <- list(f1 = matrix(runif(n.tr*10), ncol = 10), f2 = matrix(runif(n.tr*22), ncol = 22))
sOut <- fgp_BB3(sIn, fIn, n.tr)
m1 <- fgpm(sIn = sIn, fIn = fIn, sOut = sOut)

# deleting two points
ind.dl <- sample(1:m1@n.tot, 2)
m1up <- update(m1, ind.dl = ind.dl)

# adding five points
n.nw <- 5
sIn.nw <- matrix(runif(n.nw * m1@ds), nrow = n.nw)
fIn.nw <- list(f1 = matrix(runif(n.nw*10), ncol = 10), f2 = matrix(runif(n.nw*22), ncol = 22))
sOut.nw <- fgp_BB3(sIn.nw, fIn.nw, n.nw)
m1up <- update(m1, sIn.nw = sIn.nw, fIn.nw = fIn.nw, sOut.nw = sOut.nw)


# substitution of data points______________________________________________________________
# building the model
set.seed(100)
n.tr <- 25
sIn <- expand.grid(x1 = seq(0,1,length = sqrt(n.tr)), x2 = seq(0,1,length = sqrt(n.tr)))
fIn <- list(f1 = matrix(runif(n.tr*10), ncol = 10), f2 = matrix(runif(n.tr*22), ncol = 22))
sOut <- fgp_BB3(sIn, fIn, n.tr)
m1 <- fgpm(sIn = sIn, fIn = fIn, sOut = sOut)

# generating substituting input data for updating
n.sb <- 2
sIn.sb <- matrix(runif(n.sb * m1@ds), nrow = n.sb)
fIn.sb <- list(f1 = matrix(runif(n.sb*10), ncol = 10), f2 = matrix(runif(n.sb*22), ncol = 22))

# generating substituting output data for updating
sOut.sb <- fgp_BB3(sIn.sb, fIn.sb, n.sb)

# generating indices for substitution
ind.sb <- sample(1:(m1@n.tot), n.sb)

# updating all, the scalar inputs, functional inputs and the output
m1up <- update(m1, sIn.sb = sIn.sb, fIn.sb = fIn.sb, sOut.sb = sOut.sb, ind.sb = ind.sb)

# updating only some of the data structures
m1up1 <- update(m1, sIn.sb = sIn.sb, ind.sb = ind.sb) # only the scalar inputs
m1up2 <- update(m1, sOut.sb = sOut.sb, ind.sb = ind.sb) # only the output
m1up3 <- update(m1, sIn.sb = sIn.sb, sOut.sb = sOut.sb, ind.sb = ind.sb) # the scalar inputs
                                                                         # and the output


# substitution of hyperparameters__________________________________________________________
# building the model
set.seed(100)
n.tr <- 25
sIn <- expand.grid(x1 = seq(0,1,length = sqrt(n.tr)), x2 = seq(0,1,length = sqrt(n.tr)))
fIn <- list(f1 = matrix(runif(n.tr*10), ncol = 10), f2 = matrix(runif(n.tr*22), ncol = 22))
sOut <- fgp_BB3(sIn, fIn, n.tr)
m1 <- fgpm(sIn = sIn, fIn = fIn, sOut = sOut)

# defining hyperparameters for substitution
var.sb <- 3
ls_s.sb <- c(2.44, 1.15)
ls_f.sb <- c(5.83, 4.12)

# updating the model
m1up <- update(m1, var.sb = var.sb, ls_s.sb = ls_s.sb, ls_f.sb = ls_f.sb)


# re-estimation of hyperparameters_________________________________________________________
# building the model
set.seed(100)
n.tr <- 25
sIn <- expand.grid(x1 = seq(0,1,length = sqrt(n.tr)), x2 = seq(0,1,length = sqrt(n.tr)))
fIn <- list(f1 = matrix(runif(n.tr*10), ncol = 10), f2 = matrix(runif(n.tr*22), ncol = 22))
sOut <- fgp_BB3(sIn, fIn, n.tr)
m1 <- fgpm(sIn = sIn, fIn = fIn, sOut = sOut)

# re-estimating the hyperparameters
m1up <- update(m1, var.re = TRUE) # only the variance
m1up <- update(m1, ls_s.re = TRUE) # only the scalar length-scale parameters
m1up <- update(m1, ls_s.re = TRUE, ls_f.re = TRUE) # all length-scale parameters
m1up <- update(m1, var.re = TRUE, ls_s.re = TRUE, ls_f.re = TRUE) # all hyperparameters

# }

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