| RQ.Kernel {rkriging} | R Documentation |
Rational Quadratic (RQ) Kernel
Description
This function specifies the Rational Quadratic (RQ) kernel.
Usage
RQ.Kernel(lengthscale, alpha = 1)
Arguments
lengthscale |
a vector for the positive length scale parameters |
alpha |
a positive scalar for the scale mixture parameter that controls the relative weighting of large-scale and small-scale variations |
Details
The Rational Quadratic (RQ) kernel is given by
k(r;\alpha)=\left(1+\frac{r^2}{2\alpha}\right)^{-\alpha},
where \alpha is the scale mixture parameter and
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.
As \alpha\to\infty, it converges to the Gaussian.Kernel.
Value
A Rational Quadratic (RQ) 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
MultiplicativeRQ.Kernel, Get.Kernel, Evaluate.Kernel.
Examples
n <- 5
p <- 3
X <- matrix(rnorm(n*p), ncol=p)
lengthscale <- c(1:p)
# approach 1
kernel <- RQ.Kernel(lengthscale, alpha=1)
Evaluate.Kernel(kernel, X)
# approach 2
kernel <- Get.Kernel(lengthscale, type="RQ", parameters=list(alpha=1))
Evaluate.Kernel(kernel, X)