Gaussian.Kernel {rkriging}

Gaussian Kernel

Description

This function specifies the Gaussian / Squared Exponential (SE) / Radial Basis Function (RBF) kernel.

Usage

Gaussian.Kernel(lengthscale)

Arguments

lengthscale

a vector for the positive length scale parameters

Details

The Gaussian kernel is given by

k(r)=\exp(-r^2/2),

where

r(x,x^{\prime})=\sqrt{\sum_{i=1}^{p}\left(\frac{x_{i}-x_{i}^{\prime}}{l_{i}}\right)^2}

is the euclidean distance between x and x^{\prime} weighted by the length scale parameters l_{i}'s.

Value

A Gaussian Kernel Class Object.

Author(s)

Chaofan Huang and V. Roshan Joseph

References

Duvenaud, D. (2014). The kernel cookbook: Advice on covariance functions.

Rasmussen, C. E. & Williams, C. K. (2006). Gaussian Processes for Machine Learning. The MIT Press.

See Also

Get.Kernel, Evaluate.Kernel.

Examples

n <- 5
p <- 3
X <- matrix(rnorm(n*p), ncol=p)
lengthscale <- c(1:p)

# approach 1
kernel <- Gaussian.Kernel(lengthscale)
Evaluate.Kernel(kernel, X)

# approach 2
kernel <- Get.Kernel(lengthscale, type="Gaussian")
Evaluate.Kernel(kernel, X)