Periodic

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

Bases: StationaryKernel

The periodic kernel.

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

\[ k(x, y) = \sigma^2 \exp \left( -\frac{1}{2} \sum_{i=1}^{D} \left(\frac{\sin (\pi (x_i - y_i)/p)}{\ell}\right)^2 \right) \]

Key reference is MacKay 1998 - “Introduction to Gaussian processes”.

Parameters:

• active_dims (list[int] | slice)

• lengthscale (AbstractUnwrappable)

• variance (AbstractUnwrappable)

• period (Any)

• n_dims (int | None)

• compute_engine (AbstractKernelComputation)