GraphKernel

class gpjax.kernels.GraphKernel(laplacian, active_dims=None, lengthscale=1.0, variance=1.0, smoothness=1.0, n_dims=None, compute_engine=<gpjax.kernels.computations.eigen.EigenKernelComputation object>)

Bases: StationaryKernel

The Matérn graph kernel defined on the vertex set of a graph.

A Matérn graph kernel defined through the graph Laplacian spectrum.

The kernel evaluates a Matérn spectral filter on each Laplacian eigenvalue \(\lambda\):

\[ \Phi(\lambda) = \left(\frac{2\nu}{\ell^2} + \lambda\right)^{-\nu}, \]

where \(\ell\) is the lengthscale parameter and \(\nu\) is the smoothness parameter. The resulting spectral weights are normalised and scaled by the variance parameter.

The key reference for this object is Borovitskiy et al. (2021).

See also

Graph Kernels fits one to a signal on a barbell graph.

Parameters:

• laplacian (Float[jaxlib._jax.Array, 'N N'] | Float[ndarray, 'N N'])

• active_dims (list[int] | slice)

• lengthscale (AbstractUnwrappable)

• variance (AbstractUnwrappable)

• smoothness (Any)

• n_dims (int | None)

• compute_engine (AbstractKernelComputation)