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.

\[k(x_1, x_2) = noise\_level \text{ if } x_i == x_j \text{ else } 0\]

Read more in the User Guide.

Added in version 0.18.

noise_levelfloat, default=1.0

Parameter controlling the noise level (variance)

noise_level_boundspair of floats >= 0 or “fixed”, default=(1e-5, 1e5)

The lower and upper bound on ‘noise_level’. If set to “fixed”, ‘noise_level’ cannot be changed during hyperparameter tuning.


>>> from sklearn.datasets import make_friedman2
>>> from sklearn.gaussian_process import GaussianProcessRegressor
>>> from sklearn.gaussian_process.kernels import DotProduct, WhiteKernel
>>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0)
>>> kernel = DotProduct() + WhiteKernel(noise_level=0.5)
>>> gpr = GaussianProcessRegressor(kernel=kernel,
...         random_state=0).fit(X, y)
>>> gpr.score(X, y)
>>> gpr.predict(X[:2,:], return_std=True)
(array([653.0..., 592.1... ]), array([316.6..., 316.6...]))
__call__(X, Y=None, eval_gradient=False)[source]#

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

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_X, 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. Only supported when Y is None.

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.

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


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_X, n_features) or list of object

Argument to the kernel.

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.


Returns whether the kernel is stationary.

property n_dims#

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

property requires_vector_input#

Whether the kernel works only on fixed-length feature vectors.


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