Radial basis function kernel

Computes the radial basis function (RBF) kernel for a distance vector or matrix: $$k(d) = \exp\left(-\frac{d^2}{2\theta^2}\right).$$ This is the correlation form of the kernel (\(k(0) = 1\)); any global variance is applied separately.

Usage

rbf_kernel(x, theta)

Arguments

x

A numeric vector or matrix of distances.

theta

A positive numeric scalar giving the length-scale parameter (the \(\ell\) of textbook presentations): correlation decays with distance over this scale, so larger values give smoother functions.

Value

A numeric vector or matrix with RBF kernel values.