ConstantKernel#

class sklearn.gaussian_process.kernels.ConstantKernel(constant_value=1.0, constant_value_bounds=(1e-05, 100000.0))[source]#

Constant kernel.

Can be used as part of a product-kernel where it scales the magnitude of the other factor (kernel) or as part of a sum-kernel, where it modifies the mean of the Gaussian process.

\[k(x_1, x_2) = constant\_value \;\forall\; x_1, x_2\]

Adding a constant kernel is equivalent to adding a constant:

kernel = RBF() + ConstantKernel(constant_value=2)

is the same as:

kernel = RBF() + 2

Read more in the User Guide.

Added in version 0.18.

Parameters:

constant_valuefloat, default=1.0: The constant value which defines the covariance: k(x_1, x_2) = constant_value
constant_value_boundspair of floats >= 0 or “fixed”, default=(1e-5, 1e5): The lower and upper bound on constant_value. If set to “fixed”, constant_value cannot be changed during hyperparameter tuning.

Examples

>>> from sklearn.datasets import make_friedman2
>>> from sklearn.gaussian_process import GaussianProcessRegressor
>>> from sklearn.gaussian_process.kernels import RBF, ConstantKernel
>>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0)
>>> kernel = RBF() + ConstantKernel(constant_value=2)
>>> gpr = GaussianProcessRegressor(kernel=kernel, alpha=5,
...         random_state=0).fit(X, y)
>>> gpr.score(X, y)
0.3696...
>>> gpr.predict(X[:1,:], return_std=True)
(array([606.1...]), array([0.24...]))

__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_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.

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.

property bounds#

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.

property hyperparameters#: Returns a list of all hyperparameter specifications.

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

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

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:

thetandarray of shape (n_dims,): The non-fixed, log-transformed hyperparameters of the kernel

Gallery examples#

Illustration of prior and posterior Gaussian process for different kernels

Iso-probability lines for Gaussian Processes classification (GPC)