"""Contains the kernel embeddings, i.e., integrals over kernels."""
from typing import Callable, Tuple
import numpy as np
from probnum.quad._integration_measures import (
GaussianMeasure,
IntegrationMeasure,
LebesgueMeasure,
)
from probnum.quad.kernel_embeddings import (
_kernel_mean_expquad_gauss,
_kernel_mean_expquad_lebesgue,
_kernel_variance_expquad_gauss,
_kernel_variance_expquad_lebesgue,
)
from probnum.randprocs.kernels import ExpQuad, Kernel
class KernelEmbedding:
"""Integrals over kernels against integration measures.
Parameters
----------
kernel:
Instance of a kernel.
measure:
Instance of an integration measure.
Raises
------
ValueError
If the input dimension of the kernel does not match the input dimension of the
measure.
"""
def __init__(self, kernel: Kernel, measure: IntegrationMeasure) -> None:
self.kernel = kernel
self.measure = measure
if self.kernel.input_shape != (self.measure.input_dim,):
raise ValueError(
"Input dimensions of kernel and measure need to be the same."
)
(self.input_dim,) = self.kernel.input_shape
# retrieve the functions for the provided combination of kernel and measure
self._kmean, self._kvar = _get_kernel_embedding(
kernel=self.kernel, measure=self.measure
)
[docs] def kernel_mean(self, x: np.ndarray) -> np.ndarray:
"""Kernel mean w.r.t. its first argument against the integration measure.
Parameters
----------
x :
*shape=(n_eval, input_dim)* -- n_eval locations where to evaluate the
kernel mean.
Returns
-------
kernel_mean :
*shape=(n_eval,)* -- The kernel integrated w.r.t. its first argument,
evaluated at locations ``x``.
"""
return self._kmean(x=x, kernel=self.kernel, measure=self.measure)
[docs] def kernel_variance(self) -> float:
"""Kernel integrated in both arguments against the integration measure.
Returns
-------
kernel_variance :
The kernel integrated w.r.t. both arguments.
"""
return self._kvar(kernel=self.kernel, measure=self.measure)
def _get_kernel_embedding(
kernel: Kernel, measure: IntegrationMeasure
) -> Tuple[Callable, Callable]:
"""Select the right kernel embedding given the kernel and integration measure.
Parameters
----------
kernel :
Instance of a kernel.
measure :
Instance of an integration measure.
Returns
-------
kernel_mean :
The kernel mean function.
kernel_variance :
The kernel variance function.
Raises
------
NotImplementedError
If the given kernel is unknown.
NotImplementedError
If the kernel embedding of the kernel-measure pair is unknown.
"""
# Exponentiated quadratic kernel
if isinstance(kernel, ExpQuad):
if isinstance(measure, GaussianMeasure):
return _kernel_mean_expquad_gauss, _kernel_variance_expquad_gauss
if isinstance(measure, LebesgueMeasure):
return _kernel_mean_expquad_lebesgue, _kernel_variance_expquad_lebesgue
raise NotImplementedError
# other kernels
raise NotImplementedError