geometric_kernels.feature_maps.deterministic

This module provides the DeterministicFeatureMapCompact, a Karhunen-Loève expansion-based feature map for those DiscreteSpectrumSpaces, for which the eigenpairs are explicitly known.

Module Contents

class geometric_kernels.feature_maps.deterministic.DeterministicFeatureMapCompact(space, num_levels, repeated_eigenvalues_laplacian=None, eigenfunctions=None)

Bases: geometric_kernels.feature_maps.base.FeatureMap

Deterministic feature map for DiscreteSpectrumSpaces for which the actual eigenpairs are explicitly available.

Parameters:

• space (geometric_kernels.spaces.DiscreteSpectrumSpace) – A DiscreteSpectrumSpace space.

• num_levels (int) – Number of levels in the kernel approximation.

• repeated_eigenvalues_laplacian (beartype.typing.Optional[lab.Numeric]) – Allowing to pass the repeated eigenvalues of the Laplacian directly, instead of computing them from the space. If provided, eigenfunctions must also be provided. Used for HodgeDiscreteSpectrumSpace.

• eigenfunctions (beartype.typing.Optional[geometric_kernels.spaces.eigenfunctions.Eigenfunctions]) – Allowing to pass the eigenfunctions directly, instead of computing them from the space. If provided, repeated_eigenvalues_laplacian must also be provided. Used for HodgeDiscreteSpectrumSpace.

__call__(X, params, normalize=True, **kwargs)

Parameters:

• X (lab.Numeric) – [N, …] points in the space to evaluate the map on.

• params (beartype.typing.Dict[str, lab.Numeric]) – Parameters of the kernel (length scale and smoothness).

• normalize (bool) – Normalize to have unit average variance. If omitted, set to True.

• **kwargs – Unused.

Returns:

Tuple(None, features) where features is an [N, O] array, N is the number of inputs and O is the dimension of the feature map.

Return type:

beartype.typing.Tuple[None, lab.Numeric]

Note

The first element of the returned tuple is the simple None and should be ignored. It is only there to support the abstract interface: for some other subclasses of FeatureMap, this first element may be an updated random key.

class geometric_kernels.feature_maps.deterministic.HodgeDeterministicFeatureMapCompact(space, num_levels)

Bases: geometric_kernels.feature_maps.base.FeatureMap

Deterministic feature map for HodgeDiscreteSpectrumSpaces for which the actual eigenpairs are explicitly available.

Corresponds to MaternHodgeCompositionalKernel and takes parameters in the same format.

Parameters:

• space (geometric_kernels.spaces.HodgeDiscreteSpectrumSpace)

• num_levels (int)

__call__(X, params, normalize=True, **kwargs)

Parameters:

• X (lab.Numeric) – [N, …] points in the space to evaluate the map on.

• params (beartype.typing.Dict[str, beartype.typing.Dict[str, lab.Numeric]]) – Parameters of the kernel (length scale and smoothness).

• normalize (bool) – Normalize to have unit average variance. If omitted, set to True.

• **kwargs – Unused.

Returns:

Tuple(None, features) where features is an [N, O] array, N is the number of inputs and O is the dimension of the feature map.

Return type:

beartype.typing.Tuple[None, lab.Numeric]

Note

The first element of the returned tuple is the simple None and should be ignored. It is only there to support the abstract interface: for some other subclasses of FeatureMap, this first element may be an updated random key.