`predict.NestedKriging`

Description

Aggregated prediction of a NestedKriging model at new points. With aggregation="NK" the prediction interpolates the design and its variance is bounded by the prior variance; the PoE family only combines submodel means/variances (cheaper).

Complexities for \(q\) prediction points, \(n\) observations, \(p\) groups: PoE family \(O(q\,n^2/p)\); NK \(O(q\,n^2)\) worst case, dominated by the cross-correlation blocks, parallelized over group pairs.

Usage

Python

# k = NestedKriging(...)
mean, stdev = k.predict(x, return_stdev=True)

R

# k = NestedKriging(...)
p <- predict(k, x, return_stdev = TRUE)
# p$mean, p$stdev

Matlab/Octave

% k = NestedKriging(...)
[mean, stdev] = k.predict(x)

Julia

# k = NestedKriging(...)
p = predict(k, x; return_stdev=true)
# p.mean, p.stdev

Arguments

Argument	Description
`x`	Numeric matrix of points where to predict (same number of columns as the design).
`return_stdev`	Logical (default `TRUE`): also return the aggregated standard deviation.

Value

The aggregated mean vector, and (optionally) the standard deviation vector. Cross-covariances between prediction points are not provided by the aggregations.

Examples

f <- function(X) apply(X, 1, function(x) sin(3 * x[1]) + cos(5 * x[2]))
set.seed(123)
X <- matrix(runif(2 * 1000), ncol = 2)
y <- f(X)
k <- NestedKriging(y, X, kernel = "matern5_2", nb_groups = 10)

x <- matrix(runif(2 * 100), ncol = 2)
p <- predict(k, x)
sqrt(mean((p$mean - f(x))^2))  # RMSE

predict.NestedKriging