Polynomial

class gpjax.kernels.Polynomial(active_dims=None, degree=2, shift=1.0, variance=1.0, n_dims=None, compute_engine=<gpjax.kernels.computations.dense.DenseKernelComputation object>)

Bases: AbstractKernel

The Polynomial kernel with variable degree.

Computes the covariance for pairs of inputs \((x, y)\) with variance \(\sigma^2\):

\[ k(x, y) = (\alpha + \sigma^2 x y)^d \]

where \(\sigma^\in \mathbb{R}_{>0}\) is the kernel’s variance parameter, shift parameter \(\alpha\) and integer degree \(d\).

Parameters:

• active_dims (list[int] | slice)

• degree (int)

• shift (Any)

• variance (Any)

• n_dims (int | None)

• compute_engine (AbstractKernelComputation)