RationalQuadratic

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

Bases: StationaryKernel

The Rational Quadratic kernel.

Computes the covariance for pairs of inputs \((x, y)\) with lengthscale parameter \(\ell\), variance \(\sigma^2\) and shape parameter \(\alpha\).

\[ k(x,y)=\sigma^2\Bigg(1+\frac{\lVert x-y\rVert^2_2}{2\alpha\ell^2}\Bigg)^{-\alpha} \]

As \(\alpha \to \infty\) this recovers the RBF kernel; it is equivalently a scale mixture of RBF kernels with a Gamma-distributed inverse squared lengthscale.

Parameters:

• active_dims (list[int] | slice)

• lengthscale (AbstractUnwrappable)

• variance (AbstractUnwrappable)

• alpha (Any)

• n_dims (int | None)

• compute_engine (AbstractKernelComputation)