sklearn.gaussian_process.kernels.WhiteKernel

class sklearn.gaussian_process.kernels.WhiteKernel(noise_level=1.0, noise_level_bounds=(1e-05, 100000.0))[source]

White kernel.

The main use-case of this kernel is as part of a sum-kernel where it explains the noise of the signal as independently and identically normally-distributed. The parameter noise_level equals the variance of this noise.

k(x_1, x_2) = noise_level if x_1 == x_2 else 0

New in version 0.18.

Parameters
noise_levelfloat, default: 1.0

Parameter controlling the noise level (variance)

noise_level_boundspair of floats >= 0, default: (1e-5, 1e5)

The lower and upper bound on noise_level

Attributes
bounds

Returns the log-transformed bounds on the theta.

hyperparameter_noise_level
hyperparameters

Returns a list of all hyperparameter specifications.

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, noise_level=1.0, noise_level_bounds=(1e-05, 100000.0))[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. Only supported when Y is None.

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 specifications.

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