rc.gpf.kernels

Contains extensions to gpflow.kernels.

Classes

MOStationary	Base class for stationary kernels, i.e. kernels that only
RBF	The radial basis function (RBF) or squared exponential kernel. The kernel equation is

Module Contents

class MOStationary(variance, lengthscales, name='Kernel', active_dims=None)

Bases: gpflow.kernels.AnisotropicStationary, gpflow.kernels.Kernel

Base class for stationary kernels, i.e. kernels that only depend on

d = x - x’

Derived classes should implement K_d(self, d): Returns the kernel evaluated on d, which is the pairwise difference matrix, scaled by the lengthscale parameter ℓ (i.e. [(X - X2ᵀ) / ℓ]). The last axis corresponds to the input dimension.

property lengthscales_neat

The kernel lengthscales as an (L,M) matrix.

K_diag(X)

The kernel diagonal.

Parameters:

X – An (N,M) Tensor.

Returns: An (L, N, L, N) Tensor.

K_unit_variance(X, X2=None)

The kernel with variance=ones(). This can be cached during optimisations where only the variance is trainable.

Parameters:

• X – An (n,M) Tensor.

• X2 – An (N,M) Tensor.

Returns: An (L,N,L,N) Tensor.

abstractmethod K_d_unit_variance(d)

The kernel with variance=ones(). This can be cached during optimisations where only the variance is trainable.

Parameters:

d – An (L,N,L,N,M) Tensor.

Returns: An (L,N,L,N) Tensor.

K_d_apply_variance(K_d_unit_variance)

Multiply the unit variance kernel by the kernel variance, and reshape.

Parameters:

K_d_unit_variance – An (L,N,L,N) Tensor.

Returns: An (LN,LN) Tensor

K_d(d)

The kernel.

Parameters:

d – An (L,N,L,N,M) Tensor.

Returns: An (LN,LN) Tensor.

class RBF(variance, lengthscales, name='Kernel', active_dims=None)

Bases: MOStationary

The radial basis function (RBF) or squared exponential kernel. The kernel equation is

k(d) = σ² exp{-½ r²}

where: r is the Euclidean distance between the input points, scaled by the lengthscales parameter ℓ. σ² is the variance parameter

Functions drawn from a MOGP with this kernel are infinitely differentiable!

K_d_unit_variance(d)

The kernel with variance=ones(). This can be cached during optimisations where only the variance is trainable.

Parameters:

d – An (L,N,L,N,M) Tensor.

Returns: An (L,N,L,N) Tensor.