Exponentiation

classsklearn.gaussian_process.kernels.Exponentiation(kernel, exponent)[source]

The Exponentiation kernel takes one base kernel and a scalar parameter \(p\) and combines them via

\[k_{exp}(X, Y) = k(X, Y) ^p\]

Note that the __pow__ magic method is overridden, so Exponentiation(RBF(), 2) is equivalent to using the ** operator with RBF() ** 2.

Read more in the User Guide.

Added in version 0.18.

Parameters:

kernelKernel

The base kernel

exponentfloat

The exponent for the base kernel

Examples

>>> from sklearn.datasets import make_friedman2
>>> from sklearn.gaussian_process import GaussianProcessRegressor
>>> from sklearn.gaussian_process.kernels import (RationalQuadratic,
...            Exponentiation)
>>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0)
>>> kernel = Exponentiation(RationalQuadratic(), exponent=2)
>>> gpr = GaussianProcessRegressor(kernel=kernel, alpha=5,
...         random_state=0).fit(X, y)
>>> gpr.score(X, y)
0.419...
>>> gpr.predict(X[:1,:], return_std=True)
(array([635.5...]), array([0.559...]))

__call__(X, Y=None, eval_gradient=False)[source]

Return the kernel k(X, Y) and optionally its gradient.

Parameters:

Xarray-like of shape (n_samples_X, n_features) or list of object

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

Yarray-like of shape (n_samples_Y, n_features) or list of object, default=None

Right argument of the returned kernel k(X, Y). If None, k(X, X) is evaluated instead.

eval_gradientbool, default=False

Determines whether the gradient with respect to the log of the kernel hyperparameter is computed.

Returns:

Kndarray of shape (n_samples_X, n_samples_Y)

Kernel k(X, Y)

K_gradientndarray of shape (n_samples_X, n_samples_X, n_dims), optional

The gradient of the kernel k(X, X) with respect to the log of the hyperparameter of the kernel. Only returned when eval_gradient is True.

propertybounds

Returns the log-transformed bounds on the theta.

Returns:

boundsndarray of shape (n_dims, 2)

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

clone_with_theta(theta)[source]

Returns a clone of self with given hyperparameters theta.

Parameters:

thetandarray of shape (n_dims,)

The hyperparameters

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.

Parameters:

Xarray-like of shape (n_samples_X, n_features) or list of object

Argument to the kernel.

Returns:

K_diagndarray of shape (n_samples_X,)

Diagonal of kernel k(X, X)

get_params(deep=True)[source]

Get parameters of this kernel.

Parameters:

deepbool, default=True

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

Returns:

paramsdict

Parameter names mapped to their values.

propertyhyperparameters

Returns a list of all hyperparameter.

is_stationary()[source]

Returns whether the kernel is stationary.

propertyn_dims

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

propertyrequires_vector_input

Returns whether the kernel is defined on discrete structures.

set_params(**params)[source]

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.

Returns:

self

propertytheta

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.

Returns:

thetandarray of shape (n_dims,)

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