PoweredExponential

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

Bases: StationaryKernel

The powered exponential family of kernels.

Computes the covariance for pairs of inputs \((x, y)\) with length-scale parameter \(\ell\), variance \(\sigma^2\) and power \(\kappa\).

\[ k(x, y)=\sigma^2\exp\Bigg(-\Big(\frac{\lVert x-y\rVert_2}{\ell}\Big)^\kappa\Bigg) \]

This also equivalent to the symmetric generalized normal distribution. See Diggle and Ribeiro (2007) - “Model-based Geostatistics”. and https://en.wikipedia.org/wiki/Generalized_normal_distribution#Symmetric_version

Parameters:

• active_dims (list[int] | slice)

• lengthscale (AbstractUnwrappable)

• variance (AbstractUnwrappable)

• power (Any)

• n_dims (int | None)

• compute_engine (AbstractKernelComputation)