rlibkriging (version 0.9-1)

leaveOneOutFun.Kriging: Compute Leave-One-Out (LOO) error for an object with S3 class "Kriging" representing a kriging model.

Description

The returned value is the sum of squares \(\sum_{i=1}^n [y_i - \hat{y}_{i,(-i)}]^2\) where \(\hat{y}_{i,(-i)}\) is the prediction of \(y_i\) based on the the observations \(y_j\) with \(j \neq i\).

Usage

# S3 method for Kriging
leaveOneOutFun(object, theta, return_grad = FALSE, bench = FALSE, ...)

Value

The leave-One-Out value computed for the given vector

\(\boldsymbol{\theta}\) of correlation ranges.

Arguments

object

A Kriging object.

theta

A numeric vector of range parameters at which the LOO will be evaluated.

return_grad

Logical. Should the gradient (w.r.t. theta) be returned?

bench

Logical. Should the function display benchmarking output

...

Not used.

Author

Yann Richet

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)

k <- Kriging(y, X, kernel = "matern3_2", objective = "LOO", optim="BFGS")
print(k)

loo <-  function(theta) leaveOneOutFun(k, theta)$leaveOneOut
t <-  seq(from = 0.001, to = 2, length.out = 101)
plot(t, loo(t), type = "l")
abline(v = k$theta(), col = "blue")