class sklearn.gaussian_process.kernels.Kernel[source]#

Base class for all kernels.

Added in version 0.18.


>>> from sklearn.gaussian_process.kernels import Kernel, RBF
>>> import numpy as np
>>> class CustomKernel(Kernel):
...     def __init__(self, length_scale=1.0):
...         self.length_scale = length_scale
...     def __call__(self, X, Y=None):
...         if Y is None:
...             Y = X
...         return np.inner(X, X if Y is None else Y) ** 2
...     def diag(self, X):
...         return np.ones(X.shape[0])
...     def is_stationary(self):
...         return True
>>> kernel = CustomKernel(length_scale=2.0)
>>> X = np.array([[1, 2], [3, 4]])
>>> print(kernel(X))
[[ 25 121]
 [121 625]]
abstract __call__(X, Y=None, eval_gradient=False)[source]#

Evaluate the kernel.

property bounds#

Returns the log-transformed bounds on the theta.

boundsndarray of shape (n_dims, 2)

The log-transformed bounds on the kernel’s hyperparameters theta


Returns a clone of self with given hyperparameters theta.

thetandarray of shape (n_dims,)

The hyperparameters

abstract diag(X)[source]#

Returns the diagonal of the kernel k(X, X).

The result of this method is identical to np.diag(self(X)); however, it can be evaluated more efficiently since only the diagonal is evaluated.

Xarray-like of shape (n_samples,)

Left argument of the returned kernel k(X, Y)

K_diagndarray of shape (n_samples_X,)

Diagonal of kernel k(X, X)


Get parameters of this kernel.

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.


Parameter names mapped to their values.

property hyperparameters#

Returns a list of all hyperparameter specifications.

abstract is_stationary()[source]#

Returns whether the kernel is stationary.

property n_dims#

Returns the number of non-fixed hyperparameters of the kernel.

property requires_vector_input#

Returns whether the kernel is defined on fixed-length feature vectors or generic objects. Defaults to True for backward compatibility.


Set the parameters of this kernel.

The method works on simple kernels as well as on nested kernels. The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

property theta#

Returns the (flattened, log-transformed) non-fixed hyperparameters.

Note that theta are typically the log-transformed values of the kernel’s hyperparameters as this representation of the search space is more amenable for hyperparameter search, as hyperparameters like length-scales naturally live on a log-scale.

thetandarray of shape (n_dims,)

The non-fixed, log-transformed hyperparameters of the kernel