Matern52.Kernel: Matern(5/2) Kernel
| Matern52.Kernel | R Documentation |
Matern(5/2) Kernel
Description
This function specifies the Matern kernel with smoothness parameter \nu=5/2.
Usage
Matern52.Kernel(lengthscale)
Arguments
lengthscale |
a vector for the positive length scale parameters |
Details
The Matern(5/2) kernel is given by
k(r)=(1+\sqrt{5}r+5r^2/3)\exp(-\sqrt{5}r),
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 Matern(5/2) 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 <- Matern52.Kernel(lengthscale)
Evaluate.Kernel(kernel, X)
# approach 2
kernel <- Get.Kernel(lengthscale, type="Matern52")
Evaluate.Kernel(kernel, X)
