sklearn.gaussian_process.kernels.Exponentiation¶

class sklearn.gaussian_process.kernels.Exponentiation(kernel, exponent)[source]¶

Exponentiate kernel by given exponent.

The resulting kernel is defined as k_exp(X, Y) = k(X, Y) ** exponent

New in version 0.18.

Parameters

kernelKernel object

The base kernel

exponentfloat

The exponent for the base kernel

Attributes

bounds

Returns the log-transformed bounds on the theta.

hyperparameters

Returns a list of all hyperparameter.

n_dims

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

theta

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

Methods

__call__(self, X[, Y, eval_gradient])	Return the kernel k(X, Y) and optionally its gradient.
clone_with_theta(self, theta)	Returns a clone of self with given hyperparameters theta.
diag(self, X)	Returns the diagonal of the kernel k(X, X).
get_params(self[, deep])	Get parameters of this kernel.
is_stationary(self)	Returns whether the kernel is stationary.
set_params(self, \*\*params)	Set the parameters of this kernel.

__init__(self, kernel, exponent)[source]¶

Initialize self. See help(type(self)) for accurate signature.

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

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

Parameters

Xarray, shape (n_samples_X, n_features)

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

Yarray, shape (n_samples_Y, n_features), (optional, default=None)

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

eval_gradientbool (optional, default=False)

Determines whether the gradient with respect to the kernel hyperparameter is determined.

Returns

Karray, shape (n_samples_X, n_samples_Y)

Kernel k(X, Y)

K_gradientarray (opt.), shape (n_samples_X, n_samples_X, n_dims)

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

property bounds¶

Returns the log-transformed bounds on the theta.

Returns

boundsarray, shape (n_dims, 2)

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

clone_with_theta(self, theta)[source]¶

Returns a clone of self with given hyperparameters theta.

Parameters

thetaarray, shape (n_dims,)

The hyperparameters

diag(self, 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, shape (n_samples_X, n_features)

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

Returns

K_diagarray, shape (n_samples_X,)

Diagonal of kernel k(X, X)

get_params(self, deep=True)[source]¶

Get parameters of this kernel.

Parameters

deepboolean, optional

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

Returns

paramsmapping of string to any

Parameter names mapped to their values.

property hyperparameters¶

Returns a list of all hyperparameter.

is_stationary(self)[source]¶

Returns whether the kernel is stationary.

property n_dims¶

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

set_params(self, **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

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.

Returns

thetaarray, shape (n_dims,)

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