RBF

class gpjax.kernels.RBF(active_dims=None, lengthscale=1.0, variance=1.0, n_dims=None, compute_engine=<gpjax.kernels.computations.dense.DenseKernelComputation object>)

Bases: StationaryKernel

The Radial Basis Function (RBF) kernel.

Computes the covariance for pair of inputs \((x, y)\) with lengthscale parameter \(\ell\) and variance \(\sigma^2\):

\[ k(x,y)=\sigma^2\exp\Bigg(- \frac{\lVert x - y \rVert^2_2}{2 \ell^2} \Bigg) \]

Parameters:

• active_dims (list[int] | slice)

• lengthscale (AbstractUnwrappable)

• variance (AbstractUnwrappable)

• n_dims (int | None)

• compute_engine (AbstractKernelComputation)

property spectral_density: MultivariateNormal

The spectral measure \(\mathcal{N}(\boldsymbol{0}, \mathrm{diag}(\ell)^{-2})\).