Product#

class sklearn.gaussian_process.kernels.Product(k1, k2)[source]#

The Product kernel takes two kernels \(k_1\) and \(k_2\) and combines them via

\[k_{prod}(X, Y) = k_1(X, Y) * k_2(X, Y)\]

Note that the __mul__ magic method is overridden, so Product(RBF(), RBF()) is equivalent to using the * operator with RBF() * RBF().

Read more in the User Guide.

Added in version 0.18.

Parameters:

k1Kernel: The first base-kernel of the product-kernel
k2Kernel: The second base-kernel of the product-kernel

Examples

>>> from sklearn.datasets import make_friedman2
>>> from sklearn.gaussian_process import GaussianProcessRegressor
>>> from sklearn.gaussian_process.kernels import (RBF, Product,
...            ConstantKernel)
>>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0)
>>> kernel = Product(ConstantKernel(2), RBF())
>>> gpr = GaussianProcessRegressor(kernel=kernel,
...         random_state=0).fit(X, y)
>>> gpr.score(X, y)
1.0
>>> kernel
1.41**2 * RBF(length_scale=1)

__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.

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.

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#: Returns whether the kernel is stationary.

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