runlmc.kern.rbf module

class runlmc.kern.rbf.RBF(inv_lengthscale=1, name='rbf', active_dims=None)

Bases: runlmc.kern.stationary_kern.StationaryKern

This class defines the RBF kernel \(k\).

\[k(r) = \exp \frac{-\gamma r^2}{2}\]

Parameters:

• inv_lengthscale – \(\gamma\), above.
• name –
• active_dims – see runlmc.kern.stationary_kern.StationaryKern for details.

from_dist(dists)

Parameters:dists – N-size numpy array of positive (Euclidean) distances. Returns:kernel value at each of the given distances

kernel_gradient(dists)

Let this kernel be parameterized by some parameters \(\boldsymbol\theta\in\mathbb{R}^p\). For every \(\theta_j\in\boldsymbol\theta\), at any given distance \(d\), we can compute the derivative \(\partial_{\theta_j}k(d)\). For the evaluation of this partial derivative at multiple places, \(\textbf{d}\), we call the vector of partial derivatives \(\partial_{\theta_j}k(\textbf{d})\).

Parameters:dists – a one-dimensional array of distances corresponding to \(\textbf{d}\), above. Returns:An iterable whose \(j\)-th entry is \(\partial_{\theta_j}k(\textbf{d})\).

to_gpy()

Returns:GPy version of this kernel.

update_gradient(grad)

Parameters:grad – a one-dimensional array, representing the gradient vector \(\nabla_{\boldsymbol\theta}L\) for the likelihood with respect to this kernel’s parameters, in the same order of parameters as the row order returned by kernel_gradient().