`NoiseKriging::fit`

Description

Fit a NoiseKriging Model Object with given Observations

Usage

Python

# k = NoiseKriging(kernel=...)
k.fit(y, noise, X, 
      regmodel = "constant",
      normalize = False,
      optim = "BFGS",
      objective = "LL",
      parameters = None)

R

# k = NoiseKriging(kernel=...)
k$fit(y, noise, X, 
      regmodel = "constant",
      normalize = FALSE,
      optim = "BFGS",
      objective = "LL",
      parameters = NULL)

Matlab/Octave

% k = NoiseKriging(kernel=...)
k.fit(y, noise, X, 
      regmodel = "constant",
      normalize = false,
      optim = "BFGS",
      objective = "LL",
      parameters = [])

Arguments

Argument	Description
`y`	Numeric vector of response values.
`noise`	Numeric vector of response variances.
`X`	Numeric matrix of input design.
`regmodel`	Universal NoiseKriging linear trend: `"constant"`, `"linear"`, `"interactive"`, `"quadratic"`.
`normalize`	Logical. If `TRUE` both the input matrix `X` and the response `y` in normalized to take values in the interval \([0, 1]\) .
`optim`	Character giving the Optimization method used to fit hyper-parameters. Possible values are: `"BFGS"` and `"none"` , the later simply keeping the values given in `parameters` . The method `"BFGS"` uses the gradient of the objective (note that `"BGFS10"` means 10 multi-start of BFGS).
`objective`	Character giving the objective function to optimize. Possible values are: `"LL"` for the Log-Likelihood.
`parameters`	Initial values for the hyper-parameters. When provided this must be named list with elements `"sigma2"` and `"theta"` containing the initial value(s) for the variance and for the range parameters. If `theta` is a matrix with more than one row, each row is used as a starting point for optimization.
`kernel`	Character defining the covariance model: `"exp"` , `"gauss"` , `"matern3_2"` , `"matern5_2"` .

Details

The hyper-parameters (variance and vector of correlation ranges) are estimated thanks to the optimization of a criterion given by objective , using the method given in optim. For now only the maximum-likelihood estimation is allowed. See this section for more details on the maximum-likelihood estimation.

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10 * rnorm(nrow(X)) # add noise dep. on X

k <- NoiseKriging("matern3_2")
print("before fit")
print(k)

k$fit(y,noise=(X/10)^2,X)
print("after fit")
print(k)

Results

[1] "before fit"
* covariance:
  * kernel: matern3_2
[1] "after fit"
* data: 10x[0.0455565,0.940467] -> 10x[0.152144,0.957381]
  * noise: 10x[2.07539e-05,0.00884479]
* trend constant (est.): 0.487335
* variance (est.): 0.0635381
* covariance:
  * kernel: matern3_2
  * range (est.): 0.211413
  * fit:
    * objective: LL
    * optim: BFGS