| MultiplicativeMatern.Kernel {rkriging} | R Documentation |
Multiplicative Generalized Matern Kernel
Description
This function specifies the Multiplicative Generalized Matern kernel.
Usage
MultiplicativeMatern.Kernel(lengthscale, nu = 2.01)
Arguments
lengthscale |
a vector for the positive length scale parameters |
nu |
a positive scalar parameter that controls the smoothness |
Details
The Multiplicative Generalized Matern kernel is given by
k(r;\nu)=\prod_{i=1}^{p}\frac{2^{1-\nu}}{\Gamma(\nu)}(\sqrt{2\nu}r_{i})^{\nu}K_{\nu}(\sqrt{2\nu}r_{i}),
where \nu is the smoothness parameter,
K_{\nu} is the modified Bessel function,
\Gamma is the gamma function,
and
r_{i}(x,x^{\prime})=\sqrt{\left(\frac{x_{i}-x_{i}^{\prime}}{l_{i}}\right)^2}
is the dimension-wise euclidean distances between x and x^{\prime} weighted by
the length scale parameters l_{i}'s.
Value
A Multiplicative Generalized Matern 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
Matern.Kernel, Get.Kernel, Evaluate.Kernel.
Examples
n <- 5
p <- 3
X <- matrix(rnorm(n*p), ncol=p)
lengthscale <- c(1:p)
# approach 1
kernel <- MultiplicativeMatern.Kernel(lengthscale, nu=2.01)
Evaluate.Kernel(kernel, X)
# approach 2
kernel <- Get.Kernel(lengthscale, type="MultiplicativeMatern", parameters=list(nu=2.01))
Evaluate.Kernel(kernel, X)